Professional activities

I serve as an editor for the Journals:

Numerical Linear Algebra with Applications (Wiley)

and for
Numerical Algorithms (Springer)

and for
Software Impacts (Elsevier)

and for
Mathematics, section: computational mathematics (mdpi)

Selected most recent publications

Some more recent products


D. Bertaccini, F. Durastante
Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications
Chapman & Hall/CRC Monographs and Research Notes in Mathematics, 2018.
Webpage of the book

D. Bertaccini, C. Di Fiore, P. Zellini, Complessita' e iterazione numerica, Boringhieri, 2013.

Journal papers
(for the final versions please check the website of the publishers or

D. Bertaccini, P. D'Ambra, F. Durastante, S. Filippone,
Why diffusion-based preconditioning of Richards equation works: spectral analysis and computation\ al experiments at very large scale,
Numerical Linear Algebra with Applications 2024;31:e2523. DOI: 10.1002/nla.2523
full paper

D. Bertaccini, A. Filippo,
A proposal for ranking through selective computation of centrality measures, full paper, PLoS ONE 18(9): e0289488, 2023
DOI: 10.1371/journal.pone.02894882023.

D. Bertaccini, F. Durastante
Nonlocal diffusion of variable order on complex networks,
International Journal of Computer Mathematics: Computer Systems Theory, Vol.7 (3), pp. 172-191, 2022
DOI: 10.1080/23799927.2022.2114381
full paper Keywords: network dynamics; nonlocal dynamics; superdiffusion.

M. Benzi, D. Bertaccini, F. Durastante, I. Simunec
Nonlocal network dynamics via fractional graph Laplacians
Journal of Complex Networks, Volume 8, Issue 3, June 2020.

D. Bertaccini, F. Durastante
Computing function of large matrices by a preconditioned rational Krylov method,
In: Numerical Mathematics and Advanced Applications ENUMATH 2019,
J.F. Vermolen, C. Vuik, M. Moller eds.,
Lecture Notes in Computational Science and Engineering LNCSE, volume 139, Springer, 2021 link here

D. Bertaccini, F. Durastante
Computing functions of very large matrices with small TT/QTT ranks by quadrature formulas,
Journal of Computational and Applied Mathematics (JCAM), vol. 370 (2020), 112663.

D. Bertaccini, F. Durastante
Block structured preconditioners in tensor form for the all-at-once solution of a finite volume fractional diffusion equation,
Applied Mathematics Letters 95 (2019) pp. 92--97, 2019. full paperr

L. Aceto, D. Bertaccini, F. Durastante, P. Novati
Rational Krylov methods for functions of matrices with applications to fractional partial differential equations,
Journal of Computational Physics, vol.396, pp. 470--482, 2019. full paper

D. Bertaccini, M. Popolizio, F. Durastante
Efficient approximation of functions of some large matrices by partial fraction expansions
International Journal of Computer Mathematics 96(9), pp. 1799-1817, 2019. full online paper

D. Bertaccini, F. Durastante
Efficient preconditioner updates for semilinear space-time fractional reaction-diffusion equations
In: Bini D. et al. (eds) Structured Matrices in Numerical Linear Algebra. Springer INdAM Series, vol 30. Springer, 2019.
Full paper in Researchgate: full paper

D. Bertaccini, F. Durastante
Limited memory block preconditioners for fast solution of fractional PDEs
J. Sci. Comput., 77(2), pp. 950--970, 2018. full paper and download online first.

D. Bertaccini, F. Durastante
Solving mixed classical and fractional partial differential equations using the short-memory principle and approximate inverses
Numerical Algorithms, 74(4), pp. 1061-1082, 2017 full paper .

D. Bertaccini, M. DOnatelli, F. Durastante, S. Serra-Capizzano
Optimizing a multigrid Runge-Kutta smoother for variable-coefficient convection-diffusion equations
Linear Algebra and its Applications, 533, pp.507-535, 2017.

D. Bertaccini, F. Durastante
Interpolating preconditioners for the solution of sequence of linear systems
Computers and Mathematics with Applications 72 (2016) 1118-1130 full paper.

D. Bertaccini, S. Filippone
Sparse approximate inverse preconditioners on high performance GPU platforms,
Computer e Mathematics with Applications, vol. 71, pp. 693-711, 2016 full paper.

D. Bertaccini, S. Filippone
Approximate Inverse Preconditioners for Krylov Methods on Heterogeneous Parallel Computers
In: M. Bader, A. Bode, H.-J. Bungartz, M. Gerndt, G.R. Joubert, F. Peters (eds.)
Parallel Computing: Accelerating Computational Science and Engineering (CSE).
ADVANCES IN PARALLEL COMPUTING, vol. 25, p. 183-192, 2014.
Fairfax, VA:IOS Press. ISSN: 0927-5452, doi: 10.3233/978-1-61499-381-0-183 full paper

A. Moleti, AM Al Maamury, D. Bertaccini, T. Botti, R. Sisto
Generation place of the long- and short-latency components of transient-evoked otoacoustic emissions in a nonlinear cochlear model
THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, vol. 133, p. 4098-4108, 2013. ISSN: 0001-4966, doi: 10.1121/1.4802940

D. Bertaccini, R. H. Chan, S. Morigi, F. Sgallari
An Adaptive Norm Algorithm for Image Restoration
Scale Space and Variational Methods in Computer Vision
Lecture Notes in Computer Science, 2012, Volume 6667/2012, 194-205, DOI: 10.1007/978-3-642-24785-9_17 full paper

D. Bertaccini, R. Sisto
Fast numerical solution of nonlinear nonlocal cochlear models,
Journal of Computational Physics 230 (2011) pp. 2575-2587 doi:10.1016/
Tech Report version Full paper

(with R. Sisto, A. Moleti, T. Botti and C. Shera)
Distortion products and backward-traveling waves in nonlinear active models of the cochlea
J. Acoust. Soc. Am. 129 (5) 2011.

S. Bellavia D. Bertaccini, and B. Morini
Nonsymmetric preconditioner updates in Newton-Krylov methods for nonlinear systems,
SIAM Journal on Scientific Computing Vol. 33, No. 5, pp. 2595--2619, 2011. Accepted preprint version Journal version

S. Bellavia, D. Bertaccini, B. Morini,
Quasi matrix free preconditioners in optimization and nonlinear least-squares.
In: American Institute of Physics Conference Proceedings 1281 AIP, vol. 2, p. 1036-1039, 2010.

D. Bertaccini, F. Sgallari
Updating preconditioners for nonlinear deblurring and denoising image restoration,
Applied Numerical Mathematics vol. 60, pp. 994-1006, 2010. full paper

(with R. Sisto, A. Moleti, N. Paternoster, T. Botti)
Different models of the active cochlea, and how to implement them in the state-space formalism,
Journal of Acoustical Society of America (JASA) 128, pp. 1191-1202, 2010. Full paper

D. Bertaccini, F. Sgallari
A flexible updating framework for preconditioners in PDE-based image restoration algorithms,
G. Kreiss et al. (eds.), Numerical Mathematics and Advanced Applications 2009, pp. 163--170, 2010.
DOI 10.1007/978-3-642-11795-4, Springer-Verlag Berlin Heidelberg. ISBN 978-3-642-11794-7.

(with A. Moleti, N. Paternoster, R. Sisto, F. Sanjust)
Otoacoustic emissions in time-domain solutions of nonlinear nonlocal cochlear models,
Journal of Acoustical Society of America (JASA) 126, pp. 2425-2436, 2009
selected by AIP for  V. J. Biol. Physics Res. (PHYSICAL STUDIES OF CELL MECHANICS section)
full paper

D. Bertaccini, S. Fanelli
"Computational and conditioning issues of a discrete model for cochlear sensorineural hypoacusia",
Applied Numerical Mathematics, vol. 59, pp. 1989-2001, 2009. full paper

M. Benzi, D. Bertaccini
Block Preconditioning of Real-Valued Iterative Algorithms for Complex Linear Systems,
(full paper) IMA J. Numer. Anal. 28, pp. 598-618, (2008)

D. Bertaccini, D. Calvetti
"Fast simulation of solid tumors thermal ablation treatments with a 3D reaction diffusion model",
(link Pubmed at NIH) J. Comp. Biol. Med., vol 37, pp.1173-1182, 2007.

D. Bertaccini, F. Di Benedetto
``Spectral analysis of nonsymmetric quasi-Toeplitz matrices with applications to preconditioned multistep formulas
SIAM J. Numer. Analysis 45-6, pp.2345-2367, 2007. full paper

D. Bertaccini, G. H. Golub and S. Serra-Capizzano
``Spectral analysis of a preconditioned iterative method for the convection-diffusion equation
SIAM J. Matr. Anal. Appl. 29-1, pp. 260--278, (full paper) 2007

S. Serra-Capizzano, D. Bertaccini, and G. Golub
How to deduce a proper eigenvalue cluster from a proper singular value cluster in the non-normal case
SIAM J. on Matrix Analysis and Applications Vol. 27-1, pp. 82-86, 2005 (full paper).

D. Bertaccini, Y. Wen and M. K. Ng
The Eigenvalues of Preconditioned Matrices for Linear Multistep Formulas in Boundary Value Form
Numerical Linear Algebra with Applications (final preprint) vol. 12, pp. 315–325, 2005.

D. Bertaccini, G. H. Golub, S. Serra-Capizzano and C. Tablino-Possio
``Preconditioned HSS methods for the solution of non-Hermitian positive definite linear systems and applications to the discrete convection-diffusion equation''
Numerische Mathematik vol.99-3, pp. 441--484, 2005 (full paper) and Stanford University report no. SCCM-02-11 (report)

D. Bertaccini,
Efficient preconditioning for sequences of parametric complex symmetric linear systems
ETNA, vol. 18, pp.49-64, (full paper) 2004

M. Benzi, D. Bertaccini,
Approximate inverse preconditioning for shifted linear systems
BIT, 43-2,  pp.231-244 (full paper) 2003

D. Bertaccini, Michael K. Ng
``Band-Toeplitz Preconditioned GMRES Iterations for time-dependent PDEs''
BIT, 43-5, pp.901-914. (full paper) 2003

D. Bertaccini, Michael K. Ng
``Block $\{\omega\}$-circulant preconditioners for the systems of differential equations''
Calcolo, vol. 40-2, 2003, pp.71-90. (Full paper)

D. Bertaccini,
The spectrum of circulant-like preconditioners for some general linear multistep formulas for linear boundary value problems
SIAM J. Numerical Analysis, vol.40-5, 2002, pp.1798-1822 (final preprint) (full paper)

D. Bertaccini, M. K. Ng
The Convergence Rate of Block Preconditioned Systems Arising From LMF-Based ODE Codes
BIT 41-3, pp. 433-450 (final preprint) 2001

D. Bertaccini, M. K. Ng
``Skew-Circulant Preconditioners for Systems of LMF-Based ODE Codes''
Lecture Notes in Comp. Sci. 1988, 2001, pp. 93-101 (full paper)

D. Bertaccini,
Reliable preconditioned iterative linear solvers for some integrators
Numerical Linear Algebra 8-2, 2001, p.111-125 (full paper)

D. Bertaccini,
A circulant preconditioner for the systems of LMF-based ODE codes
SIAM J. Sci Comput. 22-3, 2001 (printed version), pp. 767 - 786 (full paper)