Preconditioners for Krylov subspace methods: An overview

JW Pearson, J Pestana - GAMM‐Mitteilungen, 2020 - Wiley Online Library
When simulating a mechanism from science or engineering, or an industrial process, one is
frequently required to construct a mathematical model, and then resolve this model …

[图书][B] Matrix analysis and computations

ZZ Bai, JY Pan - 2021 - SIAM
Analysis and computation, the most important and indispensable methods for processing
matrices, are closely related but two significantly different areas. The former focuses more on …

Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems

ZZ Bai, GH Golub - IMA Journal of Numerical Analysis, 2007 - academic.oup.com
We establish a class of accelerated Hermitian and skew-Hermitian splitting (AHSS) iteration
methods for large sparse saddle-point problems by making use of the Hermitian and skew …

Preconditioned MHSS iteration methods for a class of block two-by-two linear systems with applications to distributed control problems

ZZ Bai, M Benzi, F Chen… - IMA Journal of Numerical …, 2013 - academic.oup.com
We construct a preconditioned modified Hermitian and skew-Hermitian splitting (PMHSS)
iteration scheme for solving and preconditioning a class of block two-by-two linear systems …

Optimal parameters in the HSS‐like methods for saddle‐point problems

ZZ Bai - Numerical Linear Algebra with Applications, 2009 - Wiley Online Library
For the Hermitian and skew‐Hermitian splitting iteration method and its accelerated variant
for solving the large sparse saddle‐point problems, we compute their quasi‐optimal iteration …

Block preconditioning of real-valued iterative algorithms for complex linear systems

M Benzi, D Bertaccini - IMA Journal of Numerical Analysis, 2008 - ieeexplore.ieee.org
We revisit real-valued preconditioned iterative methods for the solution of complex linear
systems, with an emphasis on symmetric (non-Hermitian) problems. Different choices of the …

On inexact Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems

ZZ Bai, GH Golub, MK Ng - Linear Algebra and Its Applications, 2008 - Elsevier
We study theoretical properties of two inexact Hermitian/skew-Hermitian splitting (IHSS)
iteration methods for the large sparse non-Hermitian positive definite system of linear …

Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices

ZZ Bai, G Golub, CK Li - Mathematics of Computation, 2007 - ams.org
For the non-Hermitian and positive semidefinite systems of linear equations, we derive
necessary and sufficient conditions for guaranteeing the unconditional convergence of the …

Optimal parameter in Hermitian and skew-Hermitian splitting method for certain two-by-two block matrices

ZZ Bai, GH Golub, CK Li - SIAM Journal on Scientific Computing, 2006 - SIAM
The optimal parameter of the Hermitian/skew-Hermitian splitting (HSS) iteration method for a
real two-by-two linear system is obtained. The result is used to determine the optimal …

The GLT class as a generalized Fourier analysis and applications

S Serra-Capizzano - Linear Algebra and its Applications, 2006 - Elsevier
Recently, the class of Generalized Locally Toeplitz (GLT) sequences has been introduced
as a generalization both of classical Toeplitz sequences and of variable coefficient …