On preconditioned MHSS iteration methods for complex symmetric linear systems

Authors:
Zhong-Zhi Bai;Michele Benzi;Fang Chen
Affiliations:
State Key Laboratory of Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, People's Republic of China 100190 and Institute of Compu ...;Department of Mathematics and Computer Science, Emory University, Atlanta, USA 30322;School of Science, Xi'an University of Post and Telecommunications, Xi'an, People's Republic of China 710121
Venue:
Numerical Algorithms
Year:
2011

Citing 3
Cited 2

Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems

SIAM Journal on Matrix Analysis and Applications
Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems

Numerische Mathematik
Modified HSS iteration methods for a class of complex symmetric linear systems

Computing

Additive block diagonal preconditioning for block two-by-two linear systems of skew-Hamiltonian coefficient matrices

Numerical Algorithms
On semi-convergence of modified HSS iteration methods

Numerical Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

We propose a preconditioned variant of the modified HSS (MHSS) iteration method for solving a class of complex symmetric systems of linear equations. Under suitable conditions, we prove the convergence of the preconditioned MHSS (PMHSS) iteration method and discuss the spectral properties of the PMHSS-preconditioned matrix. Numerical implementations show that the resulting PMHSS preconditioner leads to fast convergence when it is used to precondition Krylov subspace iteration methods such as GMRES and its restarted variants. In particular, both the stationary PMHSS iteration and PMHSS-preconditioned GMRES show meshsize-independent and parameter-insensitive convergence behavior for the tested numerical examples.