Publication List

Books & Lecture Notes

  • D. Bertaccini and F. Durastante. Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications. Chapman & Hall/CRC Monographs and Research Notes in Mathematics. CRC Press, 2018. ISBN : 9781498764179. URL :
  • C. Garoni, F. Durastante, M. Mazza, and S. Serra-Capizzano. “Generalized Locally Toeplitz Sequences: A Spectral Analysis Tool for Approximated Differential Equations and Few Selected Examples”. In: XVI BSCG Notes – XVI Brazilian School of Cosmology and Gravitation, Rio de Janeiro. June 2017.

Journal articles

  • M. Benzi, D. Bertaccini, F. Durastante, and I. Simunec. “Nonlocal network
    dynamics via fractional graph Laplacians”. In: Journal of Complex Networks (2020). eprint: arXiv:1912.07288. In Press
  • C. M. Mauro and F. Durastante  “Evaluating visibility at sea: Instrumental data and historical nautical records. Mount Etna from the Calabrian Ionian coast (Italy)”. The Journal of Island and Coastal Archaeology (2020), DOI: 10.1080/15564894.2020.1755394
  • D. Bertaccini and F. Durastante. “Computing functions of very large matrices with small TT/QTT ranks by quadrature formulas”. In: Journal of Computational and Applied Mathematics, 370, (2020), DOI: 10.1016/
  • F. Durastante, “Efficient solution of time-fractional differential equations with a new adaptive multi-term discretization of the generalized Caputo–Dzherbashyan derivative”. In: Calcolo, 56(4), (2019), 36. DOI: 10.1007/s10092-019-0329-0.
  • L. Aceto, D. Bertaccini, F. Durastante, and P. Novati. “Rational Krylov methods for functions of matrices with applications to fractional partial differential equations”. In: Journal of Computational Physics 396 (2019), 470–482. DOI: 10.1016/
  • D. Bertaccini and F. Durastante “Block structured preconditioners in tensor form for the all-at-once solution of a finite volume fractional diffusion equation”. In  Applied  Mathematics Letter 95 (2019), 92–97. DOI: 10.1016/j.aml.2019.03.028.
  • D. Bertaccini and F. Durastante. “Limited Memory Block Preconditioners for Fast Solution of Fractional Partial Differential Equations”. In: Journal of Scientific Computing 77.2 (Nov. 2018), pp. 950–970. ISSN: 1573-7691. DOI : 10.1007/s10915-018-0729-3. URL:
  • D. Bertaccini, M. Popolizio, and F. Durastante. “Efficient approximation of functions of some large matrices by partial fraction expansions”. In: International Journal of Computer Mathematics (Oct. 2018). DOI: 10.1080/00207160.2018.1533123. eprint: arXiv: 1709.06351. In Press.
  • S. Cipolla, C. Di Fiore, F. Durastante, and P. Zellini. “Regularizing properties of a class of matrices including the optimal and the superoptimal preconditioners”. In: Numerical Linear Algebra with Applications 26.2 (2018). e2225 nla.2225, e2225. DOI: 10.1002/nla.2225.
    eprint: URL:
  • S. Cipolla and F. Durastante. “Fractional PDE constrained optimization: An optimize-then-discretize approach with L-BFGS and approximate inverse preconditioning”. In: Applied Numerical Mathematics 123 (2018), pp. 43–57. DOI: 10.1016/j.apnum.2017.09.001.
  • D. Bertaccini, M. Donatelli, F. Durastante, and S. Serra-Capizzano. “Optimizing a multigrid Runge–Kutta smoother for variable-coefficient convection-diffusion equations”. In: Linear Algebra and Its Applications 533 (2017), pp. 507–535. DOI: 10.1016/j.laa.2017.07.
  • D. Bertaccini and F. Durastante. “Solving mixed classical and fractional partial differential equations using short-memory principle and approximate inverses”. In: Numerical Algorithms 74.4 (Apr. 2017), pp. 1061–1082. ISSN: 1572-9265. DOI: 10.1007/s11075-016-0186-8. URL:
  • D. Bertaccini and F. Durastante. “Interpolating preconditioners for the solution of sequence of linear systems”. In: Computers and Mathematics with Applications 72.4 (2016), pp. 1118–1130. DOI: 10.1016/j.camwa.2016.06.023.


  • D. Bertaccini and F. Durastante. “Efficient Preconditioner Updates for Semilinear Space-Time Fractional Reaction-Diffusion Equations”. In: Structured Matrices in Numerical Linear Algebra. Ed. by Bini D., Di Benedetto F., Tyrtyshnikov E.,  and M. Van Barel.  Cham: Springer International Publishing, 2019, pp. 285-302. Springer INdAM Series, vol 30. ISBN: 978-3-030-04087-1. DOI: 10.1007/978-3-030-04088-8_15. URL:
  • F. Durastante and S. Cipolla. “Fractional PDE Constrained Optimization: Box and Sparse Constrained Problems”. In: Numerical Methods for Optimal Control Problems. Ed. by Maurizio Falcone, Roberto Ferretti, Lars Grüne, and William M. McEneaney. Cham: Springer International Publishing, 2018, pp. 111–135. Springer INdAM Series, vol 29. ISBN: 978-3-030-01959-4. DOI: 10.1007/978-3-030-01959-4_6. URL:
  • F. Durastante. “Interpolant Update of Preconditioners for Sequences of Large Linear Systems”. In: Mathematical Methods, Computational Techniques and Intelligent Systems (MAMECTIS ’15). Vol. 41. WSEAS Press. 2015, pp. 40–47.

Preprints, Submitted and In Preparation

  • P. Birken, F. Durastante, and S. Serra-Capizzano. “Computing the GLT Symbol for PDEs Discretized on Regular Grids”.  In Preparation.
  • S. Cipolla, M. Donatelli, and F. Durastante. “Matrix–Function Preconditioners for Iterative Regularization”.  In Preparation.
  • P. Dell’Acqua and F. Durastante. “New periodicontinuous boundary conditions for fast and accurate image restoration”. In Preparation.
  • S. Cipolla, F. Durastante, and F. Tudisco. “Nonlocal PageRank”. In Preparation.
  • D. Bertaccini and F. Durastante. “Computing function of large matrices by a preconditioned rational Krylov method”. Submitted.
  • F. Durastante and I. Furci. “Spectral Analysis of Saddle-point Matrices from Optimization problems with Elliptic PDE Constraints”. (Mar. 2019).  eprint: arXiv:1903.01869. Submitted.
Review and Editorial Board

Associate Editor for Journal of Mathematical Modeling (JMM) (ISSN: 2345-394X).
Reviewer for: Numerical Algorithms (20), Applied Numerical Mathematics (4), Applied Mathematics and Computation (3), Calcolo (2), Mathematics – MDPI (2), Symmetry – MDPI (3), Numerical Mathematics: Theory, Methods and Applications (1), Boundary Value Problems (1), FILOMAT (1), Journal of Inequalities and Applications (1), Euro–Par 2018 (1), International Journal of  Computer Mathematics (1), AMS/MathSciNet (Mathematical Reviews).

Convegni e Workshop
  1. 17th International Conference on Mathematical Methods, Comptutational Techniques and Intelligent Systems (MAMECTIS ’15), Tenerife, Canary Islands, Spain – January 10-12, 2015
    • Tenuto il talk dal titolo “Interpolant update of preconditioners for sequences of large linear systems
  2. 13th EUROPT Workshop on Advances in Continuous Optimization, 8-10 July, 2015: Edinburgh
    • Tenuto il talk dal titolo “The update of sequences of some incomplete decompositions matrices for preconditioning
  3. Innovation & Growth, a process entangling public and private sectors
    September 17-18, 2015: Auditorium Spazio Como – Como IT
  4. 9th Workshop SDS2016 – Structural Dynamical Systems: Computational Aspects, 14-17 June, 2016: Capitolo, Monopoli, Italy.
    • Presentato il poster dal titolo “Solving mixed classical and fractional partial differential equations Short-memory principle and approximate inverses
  5. Due Giorni di Algebra Lineare Numerica, 16-17 Febbraio, 2016, Como (CO), Italia
    • Tenuto il talk dal titolo “Solving mixed classical and fractional partial differential equations Short-memory principle and approximate inverses
  6. Numerical methods for optimal control problems: algorithms, analysis and applications, Roma, June, 19-23, 2017, Istituto Nazionale di Alta Matematica – INdAM
    • Tenuto il talk dal titolo “Fractional PDEs Constrained Optimization: An optimize-then-discretize approach with L-BFGS and Approximate Inverse Preconditioning
  7. Structured Matrices in Numerical Linear Algebra: Analysis, Algorithms and Applications, Cortona, Italy, September 4-8, 2017 – INdAM Meeting
    • Presentati i poster dal titolo: “Fast Solution of Fractional Differential Equation” e “Fractional PDE Constrained Optimization: An optimize-then-discretize approach with L-BFGS and Approximate Inverse Preconditioning
  8. Quantitative Systems: Theory and Applications (QuaSy 2017). Como, Italy. October, 16-17, 2017.
  9. INdAM Workshop “Design of Reliable, Exact,and Application-oriented technologies for geometric Modeling and numerical Simulation (DREAMS)” INdAM, Rome, Italy, from 22 to 26,January 2018.
  10. Due giorni di Algebra Lineare Numerica e Applicazioni. Padua, Italy, from 8 to 9 February 2018.
    • Tenuto il talk dal titolo: “Fast Solution of Time-Dependent Fractional PDEs: Sparse and Limited Memory Block Preconditioners”
  11. Convegno 2018 Del Gruppo Nazionale per Il Calcolo Scientifico Dell’INDAM, Hotel Belvedere, Montecatini Terme, Italy, from 14 to 16 February 2018.
  12. SIAM conference on Applied Linear Algebra, Hong Kong, 4-8 May 2018.
    • Tenuto il talk dal titolo: “Limited memory block preconditioners for fast solution of time-dependent fractional PDEs”
  13. Calcolo Scientifico e Modelli Matematici: alla ricerca delle cose nascoste attraverso le cose manifeste 2.0, Como, 16-18 Maggio 2018
    • Presentato il poster dal titolo: “Efficient Solution of Time-Fractional Differential Equations with a New Adaptive Multi-Term Discretization of the Generalized Caputo–Dzherbashyan Derivative”
  14. 10th Workshop SDS2018, Structural Dynamical Systems: Computational Aspects, Porto Giardino Resort, Capitolo (Monopoli) – Bari, Italy, June 12-15, 2018
    • Tenuto il talk dal titolo: “Limited memory block preconditioners for fast solution of FPDEs”
  15. Congresso Nazionale SIMAI 2018, Roma, July 2-6, 2018
    • Tenuto il talk dal titolo: “Fast and reliable solution of fractional PDE constrained optimization problems”
  16. Rome-Moscow school of Matrix Methods and Applied Linear Algebra 2018, July 28-August 11 (Moscow), September 9-23 (Rome)
    • Tenuto il seminario dal titolo: “A Numerical Linear Algebra Perspective on Fractional Differential Equations”
  17. GAMM activity group on applied and numerical linear algebra workshop, Lund, Sweden, October 10–18, 2018.
    • Tenuto il talk dal titolo: “Limited memory block preconditioners for fast solution of FPDEs”.
  18. Due giorni di Algebra Lineare Numerica, Sapienza Università di Roma. February 18–19, 2019.
    • Tenuto il talk dal titolo: “Some fast algorithms for the large structured linear systems of FPDEs”
  19. International Congress on Industrial and Applied Mathematics (ICIAM2019), Valencia, Spain.
    • Minisymposium: organizer of the minisymposium “Advances in Fractional Differential Equations: Discretization Methods and Efficient Solvers”, together with M. Mazza.
    • Tenuto il talk dal titolo: “A Numerical Perspective on Fractional Differential Equations”.
  20. European Numerical Mathematics and Advanced Applications Conference 2019 (ENUMATH2019), Egmond aan Zee, The Netherlands.
    • Talk: “Spectral Analysis of Saddle-point Matrices from Optimal Control PDE Problems”
  21. School on “Mathematical and Computational Aspects of Machine Learning”. Centro di Ricerca Matematica Ennio De Giorgi, Pisa (PI), Italy. October 7-11, 2019
  22. Convegno e Assemblea Gruppo Nazionale Calcolo Scientifico 2020 GNCS–INdAM. Hotel Belvedere, Montecatini Terme (Italy). February, 11-13, 2020.
    • Talk: “Convergenza e scalabilità di un metodo multigrid algebrico con aggregazione basata sul matching di grafo:
      analisi teorica e aspetti computazionali in ambienti HPC”
  23. 16th Copper Mountain Conference On Iterative Methods. Copper Mountain, Colorado (USA). March 21-26, 2020.
    • Talk: “Finding AMG aggregates in a haystack: from maximum product matching to scalable solvers”
1First Certificate in EnglishUniversity of Cambridge (ESOL Examinations)Giugno 2008presente
2Game TheoryStanford University & The University of British ColumbiaFebbraio 2013presente
3Linear and Discrete OptimizationÉcole Polytechnique Fédérale de LausanneAprile 2013presente
4Computing for Data AnalysisJohns Hopkins UniversityOttobre 2013presente
5GamificationUniversity of PennsylvaniaMarzo 2015presente
6University Teaching 101Johns Hopkins UniversityMaggio 2015presente
7Getting Started With PythonUniversity of MichiganNovembre 2015presente
8Quantitative Biology WorkshopMITxMaggio 2016presente
Esami e Corsi
Complementi di Analisi Matematica 1 (Teoria della Misura)27Complementi di Analisi Numerica 1 (Metodi Numerici per l'Approssimazione)30
Teoria delle Rappresentazioni 130Laboratorio di Calcolo30
Metodi Numerici per le PDE30LLingua Inglese E3Idoneo
Complementi di Analisi Numerica 230Codifica e Compressione di Segnali e Immagini29
Complementi di Probabilità27Meccanica Analitica e Celeste30
Complementi di Analisi Matematica 2 (Analisi Funzionale)30Metodi Numerici per l'Ottimizzazione30L
Storia della Scienza28

Dottorato in Informatica e Matematica del Calcolo

    • Deterministic/probabilistic Dynamical systems with applications to extreme events theory, Prof. Vaienti
    • Joint spectral radius and optimization for subdivision, Prof. M. Charina
    • Introduction to Multigrid, Prof. M. Donatelli
    • Krylov subspace methods for discrete ill-posed problem, Prof. P. Novati
    • Macroscopic and Kinetic Models of Vehicular Traffic Flows, Prof. A. Tosin
    • Exploiting Hidden Structure in Matrix Computations. Algorithms and Applications
      CIME-EMS Summer School in applied mathematics
      June 22 – June 26, 2015 – Cetraro (CS)
      (Scuola seguita con borsa Full Board del CIME)
    • Computational Finance, Prof.dr. Cornelis W. Oosterlee
    • Toeplitz e Localmente Toeplitz come strumenti di indagine spettrale per EDP approssimate, Prof. S. Serra-Capizzano
    • Introduction to Isogeometric Analysis, Prof. C. Manni, Dr. F. Pelosi, Dr. H. Speleers
    • Network analysis, orthogonal polynomials, and Gauss quadrature – L. Reichel
    • Frontiers in Partial Differential Equations Analysis and Solvers
      Summer school supported by the Department of Mathematics F. Casorati (Pavia) and by Fondazione Alma Mater Ticinenis.
      May 22 – 25, 2017
    • Splines and PDEs: Recent Advances from Approximation Theory to Structured Numerical Linear Algebra
      CIME-EMS Summer School in applied mathematics
      July 3 – Jult 7, 2017 – Cetraro (CS)
      (Scuola seguita con borsa Partial Grant del CIME, estesa a Full Board)

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