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46 47<!-- End Jekyll SEO tag --> 48 49</head> 50 51 <body> 52 <div id="particles-js"> 53 <div class="header"> 54 <h1> 55 <span class="site-title">Fabio Durastante</span> 56 <span class="site-description">Associate Professor</span> 57 </h1> 58 <div class="header-icons"> 59 <a aria-label="Send email" href="mailto:[email protected]"><i class="icon fa fa-envelope"></i></a> 60 <a aria-label="My Twitter" href="https://twitter.com/CirdansHome" targe="_blank"><i class="icon fa fa-twitter"></i></a> 61 <a aria-label="My LinkedIn" target="_blank" href="https://www.linkedin.com/in/fdurastante/"><i class="icon fa fa-linkedin-square" aria-hidden="true"></i></a> 62 <a aria-label="My Github" target="_blank" href="https://github.com/Cirdans-Home"><i class="icon fa fa-github-alt" aria-hidden="true"></i></a> 63 <a aria-label="My ResearchGate" target="_blank" href="https://www.researchgate.net/profile/Fabio_Durastante2"><i class="icon fab fa-researchgate" aria-hidden="true"></i></a> 64 <a aria-label="My GoogleScholar" target="_blank" href="https://scholar.google.it/citations?user=sB3fLcMAAAAJ&hl=it"><i class="icon fab fa-google" aria-hidden="true"></i></a> 65 <a aria-label="My Orcid" target="_blank" href="https://orcid.org/0000-0002-1412-8289"><i class="icon fab fa-orcid" aria-hidden="true"></i></a> 66 </div> 67 <div class="header-links"> 68 <a class="link" href="/research.html">Research</a> 69 <a class="link" href="/projects.html">Projects</a> 70 <a class="link" href="/conferences.html">Conferences</a> 71 <a class="link" href="/code.html">Code</a> 72 <a class="link" href="/teaching.html">Teaching</a> 73 <a class="link" href="/students.html">Students&Theses</a> 74 </div> 75 </div> 76 <a class="down" href="#about" data-scroll><i class="icon fa fa-chevron-down" aria-hidden="true"></i></a> 77</div> 78 79 <section id="about"> 80 <div class="standard-page" style="text-align: justify; text-justify: inter-word;"> 81 <h1>Research</h1> 82 83My research activities are divided into different strands and projects. 84The publications are reported by subject area and project in descending 85temporal order.<br> 86 87The same information can be found on either my <a href="https://scholar.google.it/citations?user=sB3fLcMAAAAJ&hl=it" 88target="_blank"><i class="fab fa-google"> Google Scholar Profile</i></a>, my 89<a href="https://www.researchgate.net/profile/Fabio_Durastante2" target="_blank"> 90 <i class="fab fa-researchgate"> ResearchGate</i></a>, or my 91<a href="https://orcid.org/0000-0002-1412-8289" target="_blank"><i class="fab fa-orcid"> 92 Orcid</i></a> profile.<br><br> 93 94 95Solving Linear Algebra problems is a core task in pretty much every Scientific 96challenge, from the numerical solution of partial differential equations to the 97new problems arising in the analysis of larger and larger sets of data. Moreover, 98we are fastly moving towards the use of exascale-enabled HPC platforms, thus we 99need to be capable of pushing our algorithms (and codes) to work efficiently in 100this environment. This first research line deals with this type of issue, and 101more specifically with the task of solving linear systems of equations, 102$$ A \mathbf{x} = \mathbf{b}, \qquad A \in \mathbb{R}^{N \times N}, \; \mathbf{x},\mathbf{b} \in \mathbb{R}^{N}, $$ 103in which $A$ is a <em>large</em>, $N \geq 10^9$, and <em>sparse</em>, 104number on non-zero entries proportional to $N$, matrix. The key instruments are 105here <b>Krylov Subspace Methods</b>, <b>Geometric</b> and <b>Algebraic Multigrid</b> 106preconditioners, and the application of update strategies to deal with more than 107one linear system. 108<table style="width:100%"> 109 <colgroup> 110 <col span="1" style="width: 30%;"> 111 <col span="1" style="width: 70%;"> 112 </colgroup> 113 <tr> 114 <td style="text-align: center">Preconditioning for large and sparse linear systems</td> 115 <td><ul class="fa-ul"> 116 <li><span class="fa-li"><i class="fas fa-spinner fa-pulse"></i></span> 117 <strong>Bucci, A.</strong>; <strong>Durastante, F.</strong>; 118 An Equivalence result for sketched Anderson Acceleration and sketched GMRES 119 <em>Submitted</em> 2026. 120 <p style="text-align: right;"><a href="https://arxiv.org/abs/2607.04904" target="_blank"><img src="/assets/img/arxiv-square.svg" width="40px" alt="Download from arXiv"></a></p> 121 122 </li> 123 <li><span class="fa-li"><i class="fas fa-spinner fa-pulse"></i></span> 124 <strong>Lombardo, L.</strong>; <strong>Durastante, F.</strong>; 125 Evaluating Rust for Sparse Matrix Kernels in Scientific Computing 126 <em>Submitted</em> (2026). 127 <p style="text-align: right;"><a href="https://arxiv.org/abs/2606.19213" target="_blank"><img src="/assets/img/arxiv-square.svg" width="40px" alt="Download from arXiv"></a></p> 128 129 </li> 130 <li><span class="fa-li"><i class="fa-regular fa-square"></i></span> 131 <strong>Durastante, F.</strong>; <strong>Mazza, M.</strong>; 132 Low-Rank Solvers for Energy-Conserving Hamiltonian Boundary Value Methods 133 <em>Springer INdAM Series (SINDAMS, volume XX)</em>. <strong>Accepted</strong> (2026). 134 <p style="text-align: right;"><a href="http://arxiv.org/abs/2511.21597" target="_blank"><img src="/assets/img/arxiv-square.svg" width="40px" alt="Download from arXiv"></a></p> 135 136 </li> 137 <li><span class="fa-li"><i class="fa-regular fa-square"></i></span> 138 <strong>D'Ambra, P.</strong>; <strong>Durastante, F.</strong>; 139 <strong>Filippone, S.</strong>. Parallel matching-based AMG preconditioners 140 for elliptic equations discretized by IgA. 141 <em>Springer INdAM Series (SINDAMS, volume XX)</em>. <strong>Accepted</strong> (2026). 142 <p style="text-align: right;"><a href="http://arxiv.org/abs/2511.21268" target="_blank"><img src="/assets/img/arxiv-square.svg" width="40px" alt="Download from arXiv"></a></p> 143 144 </li> 145 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 146 <strong>Boella, E.</strong>; <strong>Angersbach, R.</strong>; <strong>Anton, D.</strong>; <strong>Agullo, E.</strong>; 147 <strong>Audit, E.</strong>; <strong>Avila, M.</strong>; <strong>Bernaschi, M.</strong>; <strong>Buonocore, F.</strong>; 148 <strong>Buttari, A.</strong>; <strong>Calosso, B.</strong>; <strong>Carrozzo, M.G.</strong>; <strong>Catillo, M.</strong>; <strong>Celestini, A.</strong>; 149 <strong>Celino, M.</strong>; <strong>Conrads, C.</strong>; <strong>DâAmbra, P.</strong>; <strong>Di Napoli, E.</strong>; 150 <strong>Durastante, F.</strong>; <strong>Fahad, M.</strong>; <strong>Filippone, S.</strong>; <strong>Giraud, L.</strong>; 151 <strong>Giusepponi, S.</strong>; <strong>Grandgirard, V.</strong>; <strong>Gregori, D.</strong>; <strong>Koestler, H.</strong> 152 <strong>Kollet, S.</strong>, <strong>Kruse, C.</strong>, <strong>Majone, B.</strong>, <strong>Marait, G.</strong>, <strong>Mayo-GarcÃa, R.</strong>, 153 <strong>MorÃñigo, J.-A-</strong>; <strong>Nakov, S.</strong>; <strong>Obrejan, K.</strong>; <strong>Owen, H.</strong>; 154 <strong>Pecchia, A.</strong>; <strong>Robeyns, M.</strong>; <strong>Rocco, R.</strong>; <strong>Schottenhamml, H.</strong>; 155 <strong>Anciaux Sedrakian, A.</strong>; <strong>Suffa, P.</strong>; <strong>Vacek, P.</strong>. 2026. The
156 Energy-Oriented Centre of Excellence: Invited Paper. In Proceedings of the 23rd ACM International Conference on Computing Frontiers (CF Companionâ26), 157 May 19-21, 2026, Catania, Italy. ACM, New York, NY, USA, 9 pages. 158 <a href="/bibtex/Boella2026.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 159 <a href="/papers/EoCoeACM.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a> 160 <a href="https://dl.acm.org/doi/10.1145/3801488.3806243" target="_blank">Open access</a>. 161 </li> 162 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 163 <strong>Durastante, F.</strong>; <strong>Mazza, M.</strong>; 164 Stage-Parallel Implicit Runge-Kutta methods via low-rank matrix equation corrections. 165 J Sci Comput <strong>107</strong>, (2026) no. 4 . 166 <a href="/bibtex/Durastante2026.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 167 <a href="/papers/JSC2026.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a> 168 <a href="https://github.com/Cirdans-Home/SP_IRK.jl" target="_blank"><i class="fa-solid fa-code"></i></a> 169 <a href="https://doi.org/10.1007/s10915-026-03185-z" target="_blank">Open access</a>. 170 </li> 171 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 172 <strong>D'Ambra, P.</strong>; <strong>Durastante, F.</strong>; 173 <strong>Filippone, S.</strong>. 174 PSCToolkit: Solving Sparse Linear Systems with a Large Number of GPUs. 175 <em>Emerging Technologies in Computational Sciences for Industry, Sustainability and Innovation. M2P 2023.</em> 176 Lect. Notes Comput. Sci. Eng., <strong>146</strong>. Springer, Cham. (2025). 177 <a href="/bibtex/Dambra2025b.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 178 </li> 179 </li> 180 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 181 <strong>D'Ambra, P.</strong>; <strong>Durastante, F.</strong>; 182 <strong>Filippone, S.</strong>; <strong>Massei, S.</strong>; 183 <strong>Thomas, S.</strong>; Optimal Polynomial Smoothers for Parallel AMG. 184 <em>Numer Algor</em> (2025). 185 <a href="/bibtex/Dambra2025.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
186 <a href="https://rdcu.be/eqfit" target="_blank">Read Online</a> 187 </li> 188 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 189 <strong>Owen, H.</strong>; <strong>Lehmkuhl, O.</strong>; 190 <strong>D'Ambra, P.</strong>; <strong>Durastante, F.</strong>; 191 <strong>Filippone, S.</strong>; Alya towards Exascale: Algorithmic Scalability 192 using PSCToolkit. <em>J. Supercomput</em> (2024). 193 <a href="/bibtex/Owen2024.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 194 <a href="/papers/JSC2024.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a> 195 <a href="https://doi.org/10.1007/s11227-024-05989-y" target="_blank">Open access</a> 196 </li> 197 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 198 <strong>Bertaccini, D.</strong>; <strong>D'Ambra, P.</strong>; 199 <strong>Durastante, F.</strong>; <strong>Filippone, S.</strong>; 200 Why diffusion-based preconditioning of Richards equation works: spectral 201 analysis and computational experiments at very large scale. (2023). 202 <em>Numer. Linear Algebra Appl.</em>; e2523. 203 <a href="/bibtex/Bertaccini2023.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 204 <a href="/papers/NLAA2023.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a> 205 <a href="https://doi.org/10.1002/nla.2523" target="_blank">Open access</a> 206 </li> 207 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 208 <strong>D'Ambra, P.</strong>; <strong>Durastante, F.</strong>; 209 <strong>Filippone, S.</strong>; <strong>Zikatanov, L.</strong>. 210 Automatic coarsening in Algebraic Multigrid utilizing quality measures 211 for matching-based aggregations. <i>Comput. Math. Appl.</i> <strong>144</strong> (2023), 212 290-305. <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=4615364" target="_blank"> 213 <strong>MR4615364</strong></a> 214 <a href="/bibtex/DAmbra2023c.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 215 <a href="/papers/CAMWA2023.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a> 216 <a href="https://doi.org/10.1016/j.camwa.2023.06.026" target="_blank">Open access</a> 217 </li> 218 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 219 <strong>D'Ambra, P.</strong>; <strong>Durastante, F.</strong>; 220 <strong>Ferdous, S.M.</strong>; <strong>Filippone, S.</strong>; 221 <strong>Halappanavar, M.</strong>; <strong>Pothen A.</strong>. 222 AMG Preconditioners based on Parallel Hybrid Coarsening and Multi-objective 223 Graph Matching. (2023). <em>31st Euromicro International Conference on Parallel, 224 Distributed and Network-Based Processing (PDP), Naples, Italy, 2023</em>, pp. 59-67. 225 <a href="/bibtex/Dambra2023b.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 226 </li> 227 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 228 <strong>P. D'Ambra</strong>; <strong>F. Durastante</strong>; 229 <strong>S. Filippone</strong>; Parallel Sparse Computation Toolkit. 230 <em>Software Impacts</em> <strong>15</strong> (2023), no. 100463. 231 <a href="/bibtex/Dambra2023.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a>
232 <a href="/papers/SIMPAC2023.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a> 233 <a href="https://doi.org/10.1016/j.simpa.2022.100463" target="_blank">Open Access</a>. 234 </li> 235 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 236 <strong>D'Ambra, P.</strong>; <strong>Durastante, F.</strong>; 237 <strong>Filippone, S.</strong>. 238 AMG Preconditioners for Linear Solvers towards Extreme Scale. 239 <em>SIAM J. Sci. Comput.</em> <strong> 43 </strong> (2021), 240 no. 5, S679-S703. 241 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4331965" target="_blank"> 242 <strong>MR4331965</strong></a> 243 <a href="/bibtex/Dambra2021.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 244 </li> 245 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 246 <strong>Bertaccini, D.</strong>; <strong>Durastante, F.</strong>. 247 Iterative methods and preconditioning for large and sparse linear systems 248 with applications. Monographs and Research Notes in Mathematics. 249 <em>CRC Press, Boca Raton, FL,</em> 2018. xviii+353 pp. 250 ISBN: 978-1-4987-6416-2 251 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3793630" 252 target="_blank"><strong>MR3793630</strong></a> 253 <a href="/bibtex/Bertaccini2018b.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 254 </li> 255 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 256 <strong>Bertaccini, D.</strong>; <strong>Donatelli, M.</strong>; 257 <strong>Durastante, F.</strong>; <strong>Serra-Capizzano, S.</strong>. 258 Optimizing a multigrid Runge-Kutta smoother for variable-coefficient 259 convection-diffusion equations. <em>Linear Algebra Appl.</em> 533 (2017), 260 507--535. <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3695922" 261 target="_blank"><strong>MR3695922</strong></a> 262 <a href="/bibtex/Bertaccini2017b.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 263 </li> 264 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 265 <strong>Bertaccini, D.</strong>; <strong>Durastante, F.</strong>. 266 Interpolating preconditioners for the solution of sequence of linear systems. 267 <EM>Comput. Math. Appl.</EM> <STRONG> 72 </STRONG> (2016), no. 4, 1118--1130. 268 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3529065" 269 target="_blank"><strong>MR3529065</strong></a> 270 <a href="/bibtex/Bertaccini2016.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 271 </li> 272 </ul> 273 <td> 274 </tr> 275</table> 276 277Fractional calculus is that subset of Analysis that studies the possibilities of 278defining differential operators of real or complex order. After the definition 279of such objects, the need to numerically approximate the solution of differential 280equations defined in terms of them immediately arises. The following papers deal 281with the efficient numerical solution of different formulations of such problems. 282 283<table style="width:100%"> 284 <colgroup> 285 <col span="1" style="width: 70%;"> 286 <col span="1" style="width: 30%;"> 287 </colgroup> 288 <tr> 289 <td> 290 <ul class="fa-ul"> 291 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 292 <strong>Durastante, F.</strong>; <strong>Giscard, P.-L.</strong>; 293 <strong>Pozza, S.</strong>. 294 A $\star$-Product Approach for Analytical and Numerical Solutions of Nonautonomous Linear Fractional Differential Equations. 295 <em>Fractional Calculus and Applied Analysis</em> (2026). 296 <a href="/bibtex/Durastante2026b.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 297 <a href="/papers/s13540-026-00529-2.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a> 298 <a href="https://link.springer.com/article/10.1007/s13540-026-00529-2" target="_blank">Open access</a>. 299 </li> 300 <li><span class="fa-li"><i class="fa-solid fa-book"></i></span> 301 Fractional Differential Equations: Modeling, Discretization, and Numerical Solvers. 302 Springer INdAM Series (SINDAMS, volume 50). Editors: <strong>A. Cardone</strong>, <strong>M. Donatelli</strong>, 303 <strong>F. Durastante</strong>, <strong>R. Garrappa</strong>, <strong>M. Mazza</strong>, 304 <strong>M. Popolizio</strong>. (2023). Pages XII, 146. ISBN: 978-981-19-7715-2. ISSN: 2281-518X. 305 </li> 306 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 307 <strong>Aceto, L.</strong>; <strong>Durastante, F.</strong>. Efficient 308 computation of the Wright function and its applications to fractional 309 diffusion-wave equations. <em>ESAIM Math. Model. Numer. Anal.</em> 310 <strong> 56 </strong> (2022), no. 6, 2181--2196. 311 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4516169"><strong>MR4516169</strong></a> 312 <a href="/bibtex/Aceto2022.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 313 <a href="/papers/m2an220030.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a> 314 </li> 315 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 316 <strong>Durastante, F.</strong>. Efficient solution of time-fractional 317 differential equations with a new adaptive multi-term discretization of 318 the generalized Caputo-Dzherbashyan derivative. 319 <em>Calcolo</em> <strong> 56 </strong> (2019), no. 4, Paper No. 36, 24 pp. 320 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4015149" target="_blank"> 321 <strong>MR4015149</strong></a> 322 <a href="/bibtex/Durastante2019.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 323 </li> 324 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 325 <strong>Bertaccini, D.</strong>; <strong>Durastante, F.</strong>. 326 Efficient preconditioner updates for semilinear space-time fractional 327 reaction-diffusion equations. <em> Structured matrices in numerical linear algebra, </em> 328 285--302, Springer INdAM Ser., 30, <em>Springer, Cham,</em> 2019. 329 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3931580" 330 target="_blank"><strong>MR3931580</strong></a> 331 <a href="/bibtex/Bertaccini2019c.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 332 </li> 333 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 334 <strong>Bertaccini, D.</strong>; <strong>Durastante, F.</strong> 335 Block structured preconditioners in tensor form for the all-at-once 336 solution of a finite volume fractional diffusion equation. 337 <em>Appl. Math. Lett.</em> 95 (2019), 92--97. 338 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3936774" 339 target="_blank"><strong>MR3936774</strong></a> 340 <a href="/bibtex/Bertaccini2019b.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 341 </li> 342 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 343 <strong>Bertaccini, D.</strong>; <strong>Durastante, F.</strong>. 344 Limited memory block preconditioners for fast solution of fractional partial 345 differential equations. <em>J. Sci. Comput.</em> <strong> 77 </strong> 346 (2018), no. 2, 950--970. 347 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3860196" target="_blank"> 348 <strong>MR3860196</strong></a> 349 <a href="/bibtex/Bertaccini2018.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 350 </li> 351 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 352 <strong>Bertaccini, D.</strong>; <strong>Durastante, F.</strong>. 353 Solving mixed classical and fractional partial differential equations 354 using short-memory principle and approximate inverses. 355 <em>Numer. Algorithms</em> <strong> 74 </strong> (2017), no. 4, 1061--1082. 356 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3626328" target=" 357 _blank"> 358 <strong>MR3626328</strong></a> 359 <a href="/bibtex/Bertaccini2017.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 360 </li> 361 </ul> 362 </td> 363 <td style="text-align: center">Numerical treatment of Fractional Differential Equations</td> 364 </tr> 365 </table> 366 367Numerical optimal control theory is a part of numerical optimization that deals 368with the problem of finding a <em>control</em> for either a boundary value problem 369or a dynamical system over a period of time in such a way that an objective function 370is minimized/maximized. The prototypical problem of this type has the form 371$$ (y^*,u^*) = \arg\min_{u \in \mathcal{U}} J(y,u) = \frac{1}{2}\|y - y_z\|_2^2 + \frac{\lambda}{2} \| u \|_2^2, \text{ s.t. } e(y,u) = 0,$$ 372where $\mathcal{U}$ is a function space containing the admissible controls, $y_z$ 373a target state, and $e(y,u)=0$ a boundary value problem that the quantities $y$ 374and $u$ have to satisfy. The numerical solution of such a problem is challenging 375in many ways, it mixes together optimization, differential, and linear algebra 376problems in a non-trivial way. 377 <table style="width:100%"> 378 <colgroup> 379 <col span="1" style="width: 30%;"> 380 <col span="1" style="width: 70%;"> 381 </colgroup> 382 <tr> 383 <td style="text-align: center">
383Numerical optimal control of Partial Differential Equations</td> 384 <td> 385 <ul class="fa-ul"> 386 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 387 <strong>Durastante, F.</strong>; <strong>Furci, I.</strong>. 388 Spectral analysis of saddle-point matrices from optimization problems 389 with elliptic PDE constraints. <em>Electron. J. Linear Algebra</em> 36 390 (2020), 773--798. 391 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4188673"> 392 <strong>MR4188673</strong></a> 393 <a href="https://journals.uwyo.edu/index.php/ela/article/view/5151/5191">Open Access</a>. 394 <a href="/bibtex/Durastante2020.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 395 <a href="/papers/dopico,+vol36_pp773-798.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a> 396 </li> 397 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 398 <strong>Durastante, F.</strong>; <strong>Cipolla, S.</strong>. 399 Fractional PDE constrained optimization: box and sparse constrained problems. 400 <em> Numerical methods for optimal control problems, </em> 401 111--135, Springer INdAM Ser., 29, <em>Springer, Cham,</em> 2018. 402 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3889795" 403 target="_blank"> 404 <strong>MR3889795</strong></a> 405 <a href="/bibtex/Cipolla2018b.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 406 </li> 407 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 408 <strong>Cipolla, S.</strong>; <strong>Durastante, F.</strong>. 409 Fractional PDE constrained optimization: an optimize-then-discretize 410 approach with L-BFGS and approximate inverse preconditioning. 411 <em>Appl. Numer. Math.</em> 123 (2018), 43--57. 412 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3711990" 413 target="_blank"><strong>MR3711990</strong></a> 414 <a href="/bibtex/Cipolla2018.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 415 </li> 416 </ul> 417 </td> 418 </tr> 419 </table> 420 A matrix function is simply a function which maps a matrix to another matrix, 421 indeed to maintain interesting properties one has to extend the concept of 422 scalar function to a matrix in a clever way. If, e.g., $f$ is a function 423 admitting a Taylor expansion with radius of convergence $r$, and $A$ is a 424 matrix such $\|A\| < r$ for any compatible norm $\|\cdot\|$, then $f(A)$ can 425 be defined as 426 $$ f(A) = \sum_{j=0}^{+\infty} c_k A^k, $$ 427 for $c_k$ the Taylor coefficients of $f$. Equivalently, if $A$ is diagonalizable, 428 and $f$ is defined on the eigenvalues of $A$, then 429 $$ f(A) = X f(\Lambda) X^{-1}, \qquad A = X \Lambda X^{-1}, \; f(\Lambda)_{i,i} = f(\lambda_i(A)), $$ 430 and in several other ways for more general $A$ and $f$. In any case, one of the 431 principal numerical task that one can face is the computation of Matrix-Function-vector 432 products, i.e., $\mathbf{y} = f(A)\mathbf{x}$, for $A$ a <em>large and sparse</em> 433 matrix. The following line of research deals with these kind of problems by 434 different techniques, and for different purposes (solution of Fractional 435 differential equations, network analysis, <em>etc.</em>). 436 <table style="width:100%"> 437 <colgroup> 438 <col span="1" style="width: 70%;"> 439 <col span="1" style="width: 30%;"> 440 </colgroup> 441 <tr> 442 <td> 443 <ul class="fa-ul"> 444 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 445 <strong>Aceto, L.</strong>; <strong>Durastante, F.</strong>. 446 Efficient computation of the sinc matrix function for the integration 447 of second-order differential equations. <em>Advances in Computational Mathematics</em> 448 <strong>50</strong> (6), 109 (2024). 449 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=4815175" target="_blank"> 450 <strong>MR4815175</strong></a> 451 <a href="/bibtex/Aceto2024b.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 452 <a href="https://github.com/Cirdans-Home/rationalsecondorder" target="_blank"><i class="fa-solid fa-code"></i></a> 453 </li> 454 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 455 <strong>Aceto, L.</strong>; <strong>Durastante, F.</strong>. 456 Theoretical error estimates for computing the matrix logarithm by 457 Padé-type approximants. <em>Linear Multilinear Algebra</em> (2025), no 9., 2251-2270. 458 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=4934074" target="_blank"> 459 <strong>MR4934074</strong></a> 460 <a href="/bibtex/Aceto2024.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 461 <a href="https://github.com/Cirdans-Home/padelogarithm" target="_blank"><i class="fa-solid fa-code"></i></a> 462 </li> 463 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 464 <strong>Bertaccini, D.</strong>; <strong>Durastante, F.</strong>. 465 Computing function of large matrices by a preconditioned rational Krylov 466 method. 467 <em> Numerical mathematics and advanced applications ENUMATH 2019, </em> 468 343--351, Lect. Notes Comput. Sci. Eng., 139, <em>Springer, Cham,</em> 469 [2021], 2021. <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4266513"> 470 <strong>MR4266513</strong></a> 471 <a href="/bibtex/Bertaccini2021.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 472 </li> 473 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 474 <strong>Bertaccini, D.</strong>; <strong>Durastante, F.</strong> 475 Computing functions of very large matrices with small TT/QTT ranks 476 by quadrature formulas. <em>
476J. Comput. Appl. Math.</em> 370 (2020), 477 112663, 15 pp. 478 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4046619" 479 target="_blank"> 480 <strong>MR4046619</strong></a> 481 <a href="/bibtex/Bertaccini2020.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 482 </li> 483 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 484 <strong>Aceto, L.</strong>; <strong>Bertaccini, D.</strong>; 485 <strong>Durastante, F.</strong>; <strong>Novati, P.</strong> 486 Rational Krylov methods for functions of matrices with applications 487 to fractional partial differential equations. 488 <em>J. Comput. Phys.</em> 396 (2019), 470--482. 489 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3989621" 490 target="_blank"><strong>MR3989621</strong></a> 491 <a href="/bibtex/Aceto2019.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 492 </li> 493 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 494 <strong>Bertaccini, D.</strong>; <strong>Popolizio, M.</strong>; 495 <strong>Durastante, F.</strong> Efficient approximation of functions 496 of some large matrices by partial fraction expansions. 497 <em>Int. J. Comput. Math.</em> <strong> 96 </strong> (2019), no. 9, 498 1799--1817. 499 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3960343" 500 target="_blank"><strong>MR3960343</strong></a> 501 <a href="/bibtex/Bertaccini2019.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 502 </li> 503 </ul> 504 </td> 505 <td style="text-align:center;"> Matrix-Functions </td> 506 </tr> 507 </table> 508 Network science is the study of complex networks that are nothing more than 509 graphs that are both not random and not structured, e.g., one usually does not 510 consider Cayley graphs encoding the structure of an abstract group. 511 Examples are telecommunication networks, computer networks, biological 512 networks, social networks, and many others. In each case, every actor is 513 represented by a vertex of the graph and their connections as an edge. 514 My interest in this field lies both in the modeling and the computational 515 aspects, specifically in the task of extracting information on the networked 516 phenomena by looking at the topology of the graph. 517 <table style="width:100%"> 518 <colgroup> 519 <col span="1" style="width: 30%;"> 520 <col span="1" style="width: 70%;"> 521 </colgroup> 522 <tr> 523 <td style="text-align:center">Graphs and Network Science: Complex-Networks</td> 524 <td> 525 <ul class="fa-ul"> 526 <li><span class="fa-li"><i class="fas fa-spinner fa-pulse"></i></span> 527 <strong>Durastante, F.</strong>; <strong>Meini, B.</strong>; <strong>Saluzzi, L.</strong> 528 Steering dynamic network centrality via control theory. 529 <em>Submitted</em> (2026). 530 <a href="https://github.com/Cirdans-Home/optimal-network-control" target="_blank"><i class="fa-solid fa-code"></i></a> 531 <p style="text-align: right;"><a href="http://arxiv.org/abs/2607.14610" target="_blank"><img src="/assets/img/arxiv-square.svg" width="40px" alt="Download from arXiv"></a></p> 532 533 </li> 534 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 535 <strong>Arrigo, F.</strong>; <strong>Durastante, F.</strong> 536 Walk based Laplacians for Modeling Diffusion on Complex Networks. 537 <em>J Sci Comput</em> 109, <strong>24</strong> (2026). 538 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR5119477" target="_blank"><strong>MR5119477</strong></a> 539 <a href="/bibtex/Arrigo2026.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 540 <a href="https://github.com/Cirdans-Home/walk-laplacian" target="_blank"><i class="fa-solid fa-code"></i></a> 541 <a href="/papers/JOMP2026.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a> 542 <a href="https://link.springer.com/article/10.1007/s10915-026-03427-0" target="_blank">Open Access</a> 543 </li> 544 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 545 <strong>Cipolla, S.</strong>; <strong>Durastante, F.</strong>; 546 <strong>Meini, B.</strong> 547 Enforcing Katz and PageRank Centrality Measures in Complex Networks. 548 <em>SIAM J. Math. Data Sci.</em> <strong>
5487</strong> (2025), no. 3, 1514-1539. 549 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4959962" target="_blank"><strong>MR4959962</strong></a> 550 <a href="/bibtex/Cipolla2025.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 551 <a href="https://github.com/Cirdans-Home/enforce-katz-and-pagerank" target="_blank"><i class="fa-solid fa-code"></i></a> 552 </li> 553 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 554 <strong>Benzi, M.</strong>; <strong>Durastante, F.</strong>; 555 <strong>Zigliotto, F.</strong> 556 Modelling advection on distance-weighted directed networks. 557 <em>Math. Models Methods Appl. Sci.</em> <strong>35</strong> (2025), no. 5, 558 1237-1265. <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=4896519" target="_blank"><strong>MR4896519</strong></a> 559 <a href="/bibtex/Benzi2025.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 560 <a href="https://github.com/francesco-zigliotto/graph-advection" target="_blank"><i class="fa-solid fa-code"></i></a> 561 </li> 562 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 563 <strong>Bertaccini, D.</strong>; <strong>Durastante, F.</strong> 564 Nonlocal diffusion of variable order on complex networks. 565 <em>Int. J. Comput. Math. Comput. Syst. Theory</em> <strong> 7 </strong> 566 (2022), no. 3, 172--191. 567 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4483942" target="_blank"><strong>MR4483942</strong></a> 568 <a href="/bibtex/Bianchi2022.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 569 </li> 570 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 571 <strong>Bianchi, D.</strong>; <strong>Donatelli, M.</strong>; 572 <strong>Durastante, F.</strong>; <strong>Mazza, M.</strong>. 573 Compatibility, embedding and regularization of non-local random 574 walks on graphs. <em>J. Math. Anal. Appl.</em> <strong> 511</strong> 575 (2022), no. 1, Paper No. 126020, 30 pp. 576 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4379318" target="_blank"> 577 <strong>MR4379318</strong></a> 578 <a href="/bibtex/Bianchi2022.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 579 </li> 580 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 581 <strong>Arrigo, F.</strong>; <strong>Durastante, F.</strong>. 582 MittagâLeffler Functions and their Applications in Network Science. 583 <em>SIAM J. Matrix Anal. Appl.</em> <strong> 42 </strong> (2021), 584 no. 4, 1581--1601. <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4340667" 585 target="_blank"><strong>MR4340667</strong></a> 586 <a href="/bibtex/Arrigo2021.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 587 </li> 588 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 589 <strong>Cipolla, S.</strong>; <strong>Durastante, F.</strong>; 590 <strong>Tudisco, F.</strong>. Nonlocal pagerank. 591 <em>ESAIM Math. Model. Numer. Anal.</em> <strong> 55 </strong> (2021), 592 no. 1, 77--97. 593 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4216832" 594 target="_blank"><strong>MR4216832</strong></a> 595 <a href="/bibtex/Cipolla2021b.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 596 <a href="/papers/m2an200017.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a> 597 </li> 598 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 599 <strong>Benzi, M.</strong>; <strong>Bertaccini, D.</strong>; 600 <strong>Durastante, F.</strong>; <strong>Simunec, I.</strong>. 601 Non-local network dynamics via fractional graph Laplacians. 602 <em>J. Complex Netw.</em> <strong> 8 </strong> (2020), no. 3, cnaa017, 603 29 pp. <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4130854" 604 target="_blank"><strong>MR4130854</strong></a> 605 <a href="/bibtex/Benzi2020.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 606 </li> 607 </ul> 608 </td> 609 </tr> 610 </table> 611<p> 612 Numerical algorithms for Markov chains are essential tools in the analysis of stochastic processes. 613 A Markov chain is defined by a transition matrix $ P $, where $ P_{ij} $ represents the probability 614 of moving from state $ i $ to state $ j $. A central computational task is finding the stationary 615 distribution $ \pi $, satisfying $ \pi P = \pi $ and $ \sum_i \pi_i = 1 $. Beyond stationarity, 616 algorithms also address the <em>embeddability problem</em>, which seeks a generator matrix $ Q $ 617 such that $ P = e^{Q} $, characterizing $ P $ as the discretization of a continuous-time Markov process. 618 Another important property is <em>reversibility</em>, where $ \pi_i P_{ij} = \pi_j P_{ji} $ for all $ i, j $,
619 which simplifies analysis and enables structure-preserving approximations. Additionally, computing 620 the <em>Kemeny constant</em>, defined as $ K = \sum_{j} m_{ij} \pi_j $ (independent of $ i $), where 621 $ m_{ij} $ is the expected number of steps to reach state $ j $ from $ i $, provides insight into 622 the overall mixing behavior of the chain. Efficient numerical methods, including Riemannian optimization, 623 sparse and dense linear solvers, eigendecomposition techniques, are key to tackling these challenges 624 at scale. 625</p> 626 <table style="width:100%"> 627 <colgroup> 628 <col span="1" style="width: 30%;"> 629 <col span="1" style="width: 70%;"> 630 </colgroup> 631 <tr> 632 <td style="text-align: center"> 633 Numerical methods for Markov Chains 634 </td> 635 <td> 636 <ul class="fa-ul"> 637 <li><span class="fa-li"><i class="fa-regular fa-square"></i></span> 638 <strong>Cipolla, S.</strong>; <strong>Durastante, F.</strong>; <strong>Gnazzo, M.</strong>, <strong>Meini, B.</strong>. 639 Nearest Reversible Markov Chains with Sparsity Constraints: An Optimization Approach. 640 Low-Rank Structures and Numerical Methods in Matrix and Tensor Computations. 641 <em>Springer INdAM Series (SINDAMS, volume XX)</em>. <strong>Accepted</strong> (2026). 642 <a href="https://github.com/Cirdans-Home/sparse-reversible" target="_blank"><i class="fa-solid fa-code"></i></a> 643 <p style="text-align: right;"><a href="https://arxiv.org/abs/2602.23059" target="_blank"><img src="/assets/img/arxiv-square.svg" width="40px" alt="Download from arXiv"></a></p> 644 645 </li> 646 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 647 <strong>Durastante, F.</strong>; <strong>Gnazzo, M.</strong>; <strong>Meini, B.</strong>. 648 Kemenyâs constant minimization for reversible Markov chains via structure-preserving perturbations. 649 <em>Bit Numer Math</em> <strong>66</strong> (2026), no. 59. 650 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=5134555" target="_blank"><strong>MR5134555</strong></a> 651 <a href="https://doi.org/10.1007/s10543-026-01152-6" target="_blank"><i class="fa-solid fa-unlock-keyhole"></i>Open Access </a> 652 <a href="/bibtex/Durastante2026d.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 653 <a href="https://github.com/Cirdans-Home/optimize-kemeny" target="_blank"><i class="fa-solid fa-code"></i></a> 654 <a href="/papers/s10543-026-01152-6.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a> 655 </li> 656 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 657 <strong>Durastante, F.</strong>; <strong>Gnazzo, M.</strong>, <strong>Meini, B.</strong>. 658 A Riemannian Optimization Approach for Finding the Nearest Reversible Markov Chain. 659 <em>Numer. Linear Algebra Appl.</em> <strong>33</strong> (2026), no. 4, Paper no. e70112. 660 <a href="https://mathscinet.ams.org/mathscinet/article?mr=5115561" target="_blank"><strong>MR5115561</strong></a> 661 <a href="/bibtex/Durastante2026c.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 662 <a href="https://github.com/miryamgnazzo/nearest-reversible" target="_blank"><i class="fa-solid fa-code"></i></a> 663 </li> 664 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 665 <strong>Durastante, F.</strong>; <strong>Meini, B.</strong>. 666 Stochastic $p$th root approximation of a stochastic matrix: A Riemannian 667 optimization approach. <em>SIAM J. Matrix Anal. Appl.</em> <strong> 45 </strong> (2024), 668 no. 2, 875--904. <a href="https://mathscinet.ams.org/mathscinet/article?mr=4734557" target="_blank"><strong>MR4734557</strong></a> 669 <a href="/bibtex/Meini2024.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 670 <a href="https://fdurastante.github.io/courses/markovslides/markovrootsslides.html#/" target="_blank"><i class="fa-solid fa-person-chalkboard"></i></a> 671 <a href="https://gist.github.com/Cirdans-Home/76ab38cbd922e56caebc526087569ad5" target="_blank"><i class="fa-brands fa-github-alt"></i></a> 672 <a href="https://github.com/Cirdans-Home/pth-root-stochastic" target="_blank"><i class="fa-solid fa-code"></i></a> 673 </li> 674 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 675 <strong>Bini, D. A.</strong>; <strong>Durastante, F.</strong>; 676 <strong>Kim, S.</strong>; <strong>Meini, B.</strong> 677 On Kemeny's constant and stochastic complement. <em>Linear Algebra Appl.</em> 678 <strong>
678703</strong> (2024), 137-162. <a href="https://mathscinet.ams.org/mathscinet/article?mr=4797227" target="_blank"><strong>MR4797227</strong></a> 679 <a href="/papers/LAA2024.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a> <a href="https://doi.org/10.1016/j.laa.2024.09.001" target="_blank">Open access</a> <a href="/bibtex/Bini2024.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> <a href="https://github.com/Cirdans-Home/Kemeny-and-Conquer" target="_blank"><i class="fa-brands fa-github"></i></a> 680 </li> 681 </ul> 682 </td> 683 </tr> 684 </table> 685<p>Inverse problems are involved in the task of inferring the parameters of the 686model from a set of (possibly noisy) measurements requires. These types of 687problems can be difficult to solve for several reasons, e.g., one could be 688dealing with a lack of unicity, that is: different values of parameters are 689consistent with the measurement, and discovering the parameters may be 690challenging from the computational point of view. I have done some work in using 691linear algebra techniques for a particular type of inverse problem that is 692<em>image denoise and deblurring</em>, that is the process of removing blurring 693artifacts and noise from images (e.g., somebody shook the camera while we were 694taking the photo).</p> 695 <table style="width:100%"> 696 <colgroup> 697 <col span="1" style="width: 70%;"> 698 <col span="1" style="width: 30%;"> 699 </colgroup> 700 <tr> 701 <td> 702 <ul class="fa-ul"> 703 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 704 <strong>Cipolla, S.</strong>; <strong>Donatelli, M.</strong>; 705 <strong>Durastante, F.</strong>. Regularization of Inverse 706 Problems by an Approximate MatrixâFunction Technique. 707 <em>Numer. Algorithms</em> <strong>88</strong> (2021), 1275-1308. 708 DOI. <a href="https://link.springer.com/article/10.1007/s11075-021-01076-y" target="_blank">10.1007/s11075-021-01076-y</a>. 709 <a href="/bibtex/Cipolla2021.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 710 <a href="/papers/s11075-021-01076-y.pdf" target="_blank"><i class="fa-regular "></i></a> 711 </li> 712 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 713 <strong>Cipolla, S.</strong>; <strong>Di Fiore, C.</strong>; 714 <strong>Durastante, F.</strong>; <strong>Zellini, P.</strong>. 715 Regularizing properties of a class of matrices including the optimal and 716 the superoptimal preconditioners. <em>Numer. Linear Algebra Appl.</em> 717 <strong> 26 </strong> (2019), no. 2, e2225, 17 pp. 718 <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3911025" 719 target="_blank"><strong>MR3911025</strong></a> <a href="/bibtex/Cipolla2019.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 720 </li> 721 </ul> 722 </td> 723 <td style="text-align: center"> 724 Regularization and Inverse Problems 725 </td> 726 </tr> 727 </table> 728 <p>Optimization tasks involve the process of finding the best possible solution from a vast, often 729 overwhelmingly large, set of valid options. These types of problems can be exceptionally difficult for 730 classical computers to solve because the number of potential combinations grows exponentially, making an 731 exhaustive search practically impossible. Quantum computing introduces a fundamentally different approach 732 by leveraging quantum mechanical propertiesâsuch as superposition and entanglementâto evaluate complex solution 733 spaces much more efficiently. I have done some work in exploring how quantum algorithms can be applied 734 to tackle these computationally demanding tasks, focusing on how we can harness quantum phenomena to 735 accelerate the discovery of optimal states (e.g., calculating the most efficient delivery routes 736 for a massive logistics network or optimizing complex financial portfolios). 737 </p> 738 <table style="width:100%"> 739 <colgroup> 740 <col span="1" style="width: 30%;"> 741 <col span="1" style="width: 70%;"> 742 </colgroup> 743 <tr> 744 <td style="text-align: center"> 745 Quantum Computing and Optimization 746 </td> 747 <td> 748 <ul class="fa-ul"> 749 <li><span class="fa-li"><i class="fas fa-spinner fa-pulse"></i></span> 750 <strong>Cipolla, S.</strong>; <strong>Durastante, F.</strong>. 751 Pauli-Sparse regularised Counterdiabatic Shortcuts for Linear-Ramp QAOA 752 <em>Submitted</em> (2026). 753 <p style="text-align: right;"><a href="https://arxiv.org/abs/2606.28536" target="_blank"><img src="/assets/img/arxiv-square.svg" width="40px" alt="Download from arXiv"></a></p> 754 755 </li> 756 </ul> 757 </td> 758 </tr> 759 </table> 760 <p>Mathematical methods play also a role in unexpected settings like archaeology. 761 They enable the analysis and interpretation of data, making predictions, and 762 gaining insights into quantitatives aspects. Statistical techniques are commonly 763 employed to analyze large datasets, such as excavation records, artifact distributions, 764 and survey data. These methods help archaeologists identify patterns, trends, 765 and correlations, allowing them to make inferences about past human behaviors 766 and societal structures. Mathematical modeling is also utilized to reconstruct 767 ancient landscapes, simulate settlement patterns, and explore the dynamics 768 of cultural change over time. The integration of mathematics into archaeological
769 investigations enhances the accuracy, precision, and efficiency of research, 770 contributing to a quantitative understanding of some aspects of history.</p> 771 <table style="width: 100%"> 772 <colgroup> 773 <col span="1" style="width: 70%;"> 774 <col span="1" style="width: 30%;"> 775 </colgroup> 776 <tr> 777 <td> 778 <ul class="fa-ul"> 779 <li><li><span class="fa-li"><i class="fas fa-check-square"></i></span> 780 <strong>Mauro, C.</strong>; <strong>Durastante, F.</strong>; <strong>DÃaz-Sánchez, C.</strong>. 781 A Light in the Dark: The Role of Coastal Lights in Night Navigation in Antiquity 782 <em>Journal of Eastern Mediterranean Archaeology and Heritage Studies</em> <strong>13</strong> (2025), no. 4, 367-380. 783 <a href="/bibtex/Mauro2025b.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 784 <a href="https://doi.org/10.5325/jeasmedarcherstu.13.4.0367" target="_blank"><i class="fa-solid fa-link"></i></a> 785 </li> 786 <li><li><span class="fa-li"><i class="fas fa-check-square"></i></span> 787 <strong>Mauro, C.</strong>; <strong>Durastante, F.</strong>. 788 On the use of lights in nocturnal seafaring during Antiquity 789 <em>International Journal of Nautical Archaeology</em> (2025), 1-8 pp. 790 <a href="/bibtex/Mauro2025.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 791 <a href="https://doi.org/10.1080/10572414.2025.2525130" target="_blank"><i class="fa-solid fa-link"></i></a> 792 </li> 793 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 794 <strong>Mauro, C.</strong>; <strong>Durastante, F.</strong>. 795 Nocturnal Seafaring: the Reduction of Visibility at Night and its Impact on Ancient Mediterranean Seafaring. 796 A Study Based on 8-4th Centuries BC Evidence <em>Journal of Maritime Archaeology</em>, (2024), 1-19 pp. 797 <a href="/bibtex/Mauro2024.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 798 <a href="/papers/JNA2024.pdf" target="_blank"><i class="fa-regular fa-file-pdf"></i></a> 799 <a href="https://doi.org/10.1007/s11457-023-09385-0" target="_blank">Open access</a> 800 </li> 801 <li><span class="fa-li"><i class="fas fa-check-square"></i></span> 802 <strong>Mauro, C.</strong>; <strong>Durastante, F.</strong>. 803 Evaluating visibility at sea: Instrumental data and historical nautical 804 records. Mount Etna from the Calabrian Ionian coast (Italy). 805 <em>The Journal of Island and Coastal Archaeology, 17.1</em> (2022), 806 21-42 pp. <a href="/bibtex/Mauro2022.bib" target="_blank"><i class="fa-solid fa-quote-right"></i></a> 807 </li> 808 </ul> 809 </td> 810 <td style="text-align: center">Applications, intersections, contaminations</td> 811 </tr> 812 </table> 813 814 <!-- 815 <h3> Projects </h3> 816 817<ul class="fa-ul"> 818 <li><span class="fa-li"><i class="fas fa-people-carry"></i></span> 819 Member of the Horizon Europe project "dealii-X: an Exascale Framework for Digital Twins of the Human Body", 820 funded by the European Union's Horizon 2020 research and innovation programme under <a href="https://cordis.europa.eu/project/id/101172493" target="_blank">grant agreement No 101172493</a>, 821 and financed with ⬠3 939 780,00. 822 </li> 823 <li><span class="fa-li"><i class="fas fa-coins"></i></span> 824 Fundings for ⬠4000.00 for the "Progetti Speciali per la Didattica 825 Università di Pisa 2023/24". Project: <em>High-Performance Mathematics</em>. 826 </li> 827 <li><span class="fa-li"><i class="fas fa-coins"></i></span> 828 Funding for 4950.00 ⬠for the 2024 GNCS INdAM project "Metodi di riduzione di 829 modello ed approssimazioni di rango basso per problemi alto-dimensionali". 830 P.I. C. Pagliantini. Participants: L. Aceto, F. Durastante, B, Meini, F.G. 831 Poloni, L, Robol, M, Strazzullo, A. Bucci, A. A. Casulli, L. Saluzzi, I. Simunec. 832 </li> 833 <li><span class="fa-li"><i class="fas fa-people-carry"></i></span> 834 Collaborator as research associate to the Istituto per le Applicazioni del 835 Calcolo "Mauro Picone" of the National Research Council of Italy to the 836 2024-2026 Energy Oriented Center of Excellence (EoCoE III): Fostering the European 837 Energy Transition with Exascale A Center of Excellence in Computing Applications. 838 EuroHPC Project, Horizon Europe Program for Research and Innovation. </li> 839 <li><span class="fa-li"><i class="fa-solid fa-server"></i></span> 840 EuroHPC Project DD-23-167, Sparse Matrix Computations at Extreme Scales for 841 the access to the Karolina supercomputer at the e-INFRA CZ facilities (Czech Republic), 842 from 5/12/2023. 843 </li> 844 <li><span class="fa-li"><i class="fas fa-coins"></i></span> Funding for 5600.00 ⬠845 for the 2023 GNCS INdAM project "Metodi basati su matrici e tensori strutturati 846 per problemi di algebra lineare di grandi dimensioni". P.I. S. Massei. 847 Participants: F. Durastante, L. Robol, B. Meini, F. Poloni, 848M. Benzi, B. Iannazzo, L. Aceto, I. Simunec, C. Faccio, M. Rinelli, A. 849Bucci, M. Viviani. </li> 850 <li><span class="fa-li"><i class="fa-solid fa-chalkboard-user"></i></span> Fundings for 851 ⬠5943,65 for the "Progetti Speciali per la Didattica 852 Università di Pisa 2022/23". Project: <em>Calcolo Parallelo dall'Infrastruttura alla Matematica</em>.</li> 853 <li><span class="fa-li"><i class="fa-solid fa-server"></i></span> 854 Leonardo Early Access Program (LEAP). Awarderd computing time on the 855 Leonardo HPC System for the project 856 "PSCToolkit for Sparse Matrix Computations at Extreme Scales". Principal 857 Investigator S. Filippone and Co-Principal Investigator P. D'Ambra. 858 Participants: S. Filippone, P. D'Ambra, F. Durastante, V. Cardellini, A. Celestini. 859 </li> 860 <li><span class="fa-li"><i class="fas fa-coins"></i></span>Funding for 2700.00 ⬠861 for the 2022 GNCS INdAM project "Metodi numerici per lâanalisi di modelli 862 innovativi di reti complesse" with Principal Investigator: Fabio Durastante 863 and participants: B. Meini, P. Boito, S. Massei, G. Del Corso, M. Benzi, 864 D. Bertaccini, P. D'Ambra, B. Iannazzo, A. Bucci, C. Faccio, M. Rinelli, 865 I. Simunec.</li> 866 <li><span class="fa-li"><i class="fas fa-coins"></i></span>Funding for 11656.03 ⬠867 for the project "¿Ver o no ver? Una aproximación interdisciplinar a los 868 estudios de visibilidad en el contexto de la navegación antigua (siglos IX-IV a.C.)."
869 (PR27/21-018) co-financed by the Comunidad de Madrid and the Universidad 870 Complutense. Principal Investigator C. M. Mauro. </li> 871 <li><span class="fa-li"><i class="fas fa-people-carry"></i></span> Member of 872 the Work-Package 6 (WP6) "Applications and Use cases" in the European 873 <a href="https://textarossa.eu/" target="_blank">TEXTAROSSA</a> project. 874 </li> 875 <li><span class="fa-li"><i class="fas fa-coins"></i></span> Funding for 876 15000⬠for the organization of the INdAM workshop on "Fractional Differential Equations: 877 Modeling, Discretization, and Numerical Solvers" (<a 878 href="https://fractionalworkshop.github.io/" target="_blank"> 879 https://fractionalworkshop.github.io/</a>). Organizing committee: 880 Angelamaria Cardone, Marco Donatelli, Fabio Durastante, Roberto Garrappa, 881 Mariarosa Mazza, Marina Popolizio. 882 </li> 883 <li><span class="fa-li"><i class="fas fa-people-carry"></i></span> Member of 884 the Work-Package 3 (WP3) "Scalable Solvers" in the European 885 <a href="https://www.eocoe.eu" target="_blank">EoCoE-II</a> project. 886 <ul> 887 <li>Writer for the Deliverable: ``D3.2 888 Preliminary results and performance evaluation of 889 Linear Algebra solvers'',</li> 890 <li>Contributor for the Deliverable: ``D3.3 891 Updated results and new releases of LA solvers.''</li> 892 </ul> 893 </li> 894 <li><span class="fa-li"><i class="fas fa-coins"></i></span> 895 Funding for 1200⬠for the 2020 GNCS-INDAM Project "Nonlocal models for 896 the analysis of complex networks" with Principal Investigator F. Durastante </li> 897 <li><span class="fa-li"><i class="fas fa-coins"></i></span> 898 Funding for 3400⬠for the 2019 GNCS-INDAM Project "Tecniche innovative e 899parallele per sistemi lineari e non lineari di grandi dimensioni, funzioni ed equazioni 900matriciali ed applicazioni" with Principal Investigator D. Bertaccini together 901with L. Bergamaschi, P. DâAmbra, M. Ferronato, C. Janna, F. Marcuzzi, A. 902Martinez Calomardo, V. Simoncini, M. Porcelli, D. Brandoni 903 </li> 904 <li><span class="fa-li"><i class="fas fa-coins"></i></span> 905 Funding for 4500⬠for the 2018 GNCS-INDAM project "Tecniche innovative 906per problemi di algebra lineare" with Principal Investigator D. Bertaccini together 907with D. Bini, G. Del Corso, D. Fasino, L. Gemignani, B. Iannazzo, N. 908Mastronardi, B. Meini, F. Poloni, A. Fayyaz, P. Boito, M. Fasi, I. Furci, S. 909Massei and L. Robol. 910 </li> 911 </ul> 912--> 913 <h3> Membership in scientific societies </h3> 914 915 <ul class="fa-ul"> 916 <li><span class="fa-li"><i class="fa-solid fa-people-group"></i></span> 917 Istituto Nazionale di Alta Matematica (INdAM) - Gruppo Nazionale di Calcolo Scientifico (GNCS). 918 </li> 919 <li><span class="fa-li"><i class="fa-solid fa-people-group"></i></span> 920 Società Italiana di Matematica Applicata e Industriale (SIMAI). 921 </li> 922 <li><span class="fa-li"><i class="fa-solid fa-people-group"></i></span> 923 Society of Industrial and Applied Mathematics (SIAM) - Activity group in Linear Algebra. 924 </li> 925 <li><span class="fa-li"><i class="fa-solid fa-people-group"></i></span> 926 International Linear Algebra Society (ILAS). 927 </li> 928 <li><span class="fa-li"><i class="fa-solid fa-people-group"></i></span> 929 Unione Matematica Italiana (UMI). 930 </li> 931 <li><span class="fa-li"><i class="fa-solid fa-people-group"></i></span> 932 ACM: Association for Computing Machinery. 933 </li> 934 </ul> 935 936 <h3> Collaboration Network </h3> 937 938 Most of the work described here has been done with several collaborators. I am 939 always working on expanding my network of collaborators by looking for people to 940 do interesting things with. 941 942 <iframe src="/network.html" width="100%" height="450px" style="border:none;" 943 title="Collaboration Network"></iframe> 944 945 <h3> Bibliometric indexes </h3> 946 <q>Not everything that counts can be counted, and not everything that can be counted counts.</q><br> 947 <table> 948 <tr> 949 <td><img src="/assets/img/FDhIndex.png" width="80%" alt="H-Index"></td> 950 <td><img src="/assets/img/FDSubjectAreas.png" width="80%" alt="Subject Areas"></td> 951 </tr> 952 <tr> 953 <td style="text-align: center;">(Scopus) H-Index: 10</td> 954 <td style="text-align: center;">(Scopus) Subject Areas</td> 955 </tr> 956 </table> 957 958<h2> Editorial Work </h2> 959 960I serve as editor for: 961<ul class="fa-ul"> 962 <li><span class="fa-li"><i class="fas fa-pen-nib"></i></span> <a href="http://www.springer.com/mathematics/applications/journal/40314" target="_blank">Computational and Applied Mathematics</a> (Comput. Appl. Math.)</li> 963 <li><span class="fa-li"><i class="fas fa-pen-nib"></i></span> <a href="https://jmm.guilan.ac.ir/" target="_blank">Journal of Mathematical Modeling</a> (J. Math. Model.)</li> 964</ul> 965<br> 966I have been part of the 967<ul class="fa-ul"> 968 <li><span class="fa-li"><i class="fas fa-pen-nib"></i></span> AD/AE The 7th Annual Parallel Applications Workshop, 969Alternatives To MPI+X Sunday, November 17, 2024 held in conjunction with SuperComputing 17-22 November 2024, Atlanta.</li> 970 <li><span class="fa-li"><i class="fas fa-pen-nib"></i></span> AD/AE Appendices Process & Badges committee for the I Am HPC International Conference for High Performance 971Computing, Networking, Storage, and Analysis; Denver, Colorado November 12-17, 2023.</li> 972 <li><span class="fa-li"><i class="fas fa-pen-nib"></i></span> Member of the Program Committee for the 9th International Conference on Scale Space and Variational Methods in Computer Vision May 21-25 2023, Sardinia - Italy</li> 973</ul> 974<br> 975 976I have served as reviewer for manuscripts submitted to the following journals.<br> 977<table> 978<tr> 979 <td><a href="https://www.scimagojr.com/journalsearch.php?q=25708&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=25708" alt="SCImago Journal & Country Rank" /></a> </td> 980 <td><a href="https://www.scimagojr.com/journalsearch.php?q=26425&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=26425" alt="SCImago Journal & Country Rank" /></a></td> 981 <td><a href="https://www.scimagojr.com/journalsearch.php?q=26419&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=26419" alt="SCImago Journal & Country Rank" /></a></td> 982 <td><a href="https://www.scimagojr.com/journalsearch.php?q=61774&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=61774" alt="SCImago Journal & Country Rank" /></a></td> 983</tr> 984<tr> 985 <td><a href="https://www.scimagojr.com/journalsearch.php?q=25170&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=25170" alt="SCImago Journal & Country Rank" /></a></td> 986 <td><a href="https://www.scimagojr.com/journalsearch.php?q=25307&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=25307" alt="SCImago Journal & Country Rank" /></a></td> 987 <td><a href="https://www.scimagojr.com/journalsearch.php?q=25712&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=25712" alt="SCImago Journal & Country Rank" /></a></td> 988 <td><a href="https://www.scimagojr.com/journalsearch.php?q=25713&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=25713" alt="SCImago Journal & Country Rank" /></a></td> 989</tr> 990<tr> 991 <td><a href="https://www.scimagojr.com/journalsearch.php?q=27856&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=27856" alt="SCImago Journal & Country Rank" /></a></td> 992 <td><a href="https://www.scimagojr.com/journalsearch.php?q=18534&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=18534" alt="SCImago Journal & Country Rank" /></a></td> 993 <td><a href="https://www.scimagojr.com/journalsearch.php?q=18120&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=18120" alt="SCImago Journal & Country Rank" /></a></td> 994 <td><a href="https://www.scimagojr.com/journalsearch.php?q=28067&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=28067" alt="SCImago Journal & Country Rank" /></a> </td> 995</tr> 996<tr> 997 <td><a href="https://www.scimagojr.com/journalsearch.php?q=21100422153&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=21100422153" alt="SCImago Journal & Country Rank" /></a></td> 998 <td><a href="https://www.scimagojr.com/journalsearch.php?q=26415&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=26415" alt="SCImago Journal & Country Rank" /></a></td> 999 <td><a href="https://www.scimagojr.com/journalsearch.php?q=23847&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=23847" alt="SCImago Journal & Country Rank" /></a></td> 1000 <td><a href="https://www.scimagojr.com/journalsearch.php?q=21100830702&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=21100830702" alt="SCImago Journal & Country Rank" /></a></td> 1001</tr> 1002<tr> 1003 <td><a href="https://www.scimagojr.com/journalsearch.php?q=19900193816&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=19900193816" alt="SCImago Journal & Country Rank" /></a></td> 1004 <td><a href="https://www.scimagojr.com/journalsearch.php?q=24557&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=24557" alt="SCImago Journal & Country Rank" /></a></td> 1005 <td><a href="https://www.scimagojr.com/journalsearch.php?q=19900192450&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=19900192450" alt="SCImago Journal & Country Rank" /></a></td> 1006 <td><a href="https://www.scimagojr.com/journalsearch.php?q=24557&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=24557" alt="SCImago Journal & Country Rank" /></a></td> 1007</tr> 1008<tr> 1009 <td> <a href="https://www.scimagojr.com/journalsearch.php?q=21100201542&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=21100201542" alt="SCImago Journal & Country Rank" /></a></td> 1010 <td><a href="https://www.scimagojr.com/journalsearch.php?q=28494&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=28494" alt="SCImago Journal & Country Rank" /></a></td> 1011 <td><a href="https://www.scimagojr.com/journalsearch.php?q=5000153703&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=5000153703" alt="SCImago Journal & Country Rank" /></a></td> 1012 <td><a href="https://www.scimagojr.com/journalsearch.php?q=4000149606&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=4000149606" alt="SCImago Journal & Country Rank" /></a></td> 1013</tr> 1014<tr> 1015 <td><a href="https://www.scimagojr.com/journalsearch.php?q=21100287116&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=21100287116" alt="SCImago Journal & Country Rank" /></a></td> 1016 <td><a href="https://www.scimagojr.com/journalsearch.php?q=21100927407&tip=sid&exact=no" title="SCImago Journal & Country Rank"><img border="0" src="https://www.scimagojr.com/journal_img.php?id=21100927407" alt="SCImago Journal & Country Rank" /></a></td> 1017</tr> 1018</table> 1019 1020 </div> 1021 </section> 1022 <footer class="footer"> 1023 <p>© Fabio Durastante</p> 1024 <p>Built with Jekyll and <span class="love">â¤</span></p> 1025</footer>
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