Non‐Hermitian perturbations of Hermitian matrix‐sequences and applications to the spectral analysis of the numerical approximation of partial differential equations

G Barbarino, S Serra‐Capizzano - Numerical Linear Algebra …, 2020 - Wiley Online Library
This article concerns the spectral analysis of matrix‐sequences which can be written as a
non‐Hermitian perturbation of a given Hermitian matrix‐sequence. The main result reads as …

A dimensional split preconditioner for Stokes and linearized Navier–Stokes equations

M Benzi, XP Guo - Applied Numerical Mathematics, 2011 - Elsevier
In this paper we introduce a new preconditioner for linear systems of saddle point type
arising from the numerical solution of the Navier–Stokes equations. Our approach is based …

[HTML][HTML] Sparse approximate inverse preconditioners on high performance GPU platforms

D Bertaccini, S Filippone - Computers & Mathematics with Applications, 2016 - Elsevier
Simulation with models based on partial differential equations often requires the solution of
(sequences of) large and sparse algebraic linear systems. In multidimensional domains …

Nonsymmetric preconditioner updates in Newton–Krylov methods for nonlinear systems

S Bellavia, D Bertaccini, B Morini - SIAM Journal on Scientific Computing, 2011 - SIAM
Newton–Krylov methods, a combination of Newton-like methods and Krylov subspace
methods for solving the Newton equations, often need adequate preconditioning in order to …

Modified HSS iteration methods for a class of non-Hermitian positive-definite linear systems

XX Guo, S Wang - Applied Mathematics and Computation, 2012 - Elsevier
We consider the numerical solution of a class of non-Hermitian positive-definite linear
systems by the modified Hermitian and skew-Hermitian splitting (MHSS) iteration method …

[HTML][HTML] Optimizing a multigrid Runge–Kutta smoother for variable-coefficient convection–diffusion equations

D Bertaccini, M Donatelli, F Durastante… - Linear Algebra and its …, 2017 - Elsevier
Abstract The theory of Generally Locally Toeplitz (or GLT for short) sequences of matrices is
proposed in the analysis of a multigrid solver for the linear systems generated by finite …

New multigrid smoothers for the Oseen problem

S Hamilton, M Benzi, E Haber - Numerical Linear Algebra with …, 2010 - Wiley Online Library
We investigate the performance of smoothers based on the Hermitian/skew‐Hermitian
(HSS) and augmented Lagrangian (AL) splittings applied to the Marker‐and‐Cell (MAC) …

How to deduce a proper eigenvalue cluster from a proper singular value cluster in the nonnormal case

S Serra-Capizzano, D Bertaccini, GH Golub - SIAM journal on matrix analysis …, 2005 - SIAM
We consider a generic sequence of matrices (the nonnormal case is of interest) showing a
proper cluster at zero in the sense of the singular values. By a direct use of the notion of …

A novel banded preconditioner for coupled tempered fractional diffusion equation generated from the regime-switching CGMY model

X Chen, XX Gong, ZR She, ZH She - Numerical Algorithms, 2024 - Springer
With the growing popularity of the regime-switching Lévy processes model in option pricing,
the coupled tempered fractional diffusion equation generated from this process has …

Fast numerical solution of nonlinear nonlocal cochlear models

D Bertaccini, R Sisto - Journal of Computational Physics, 2011 - Elsevier
A fast full second order time-step algorithm for some recently proposed nonlinear, nonlocal
active models for the inner ear is analyzed here. In particular, we emphasize the properties …