Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. (English) Zbl 1036.65032

Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K.

SIAM J. Matrix Anal. Appl. 24, No. 3, 603-626 (2003).

The authors discuss efficient iterative methods for large sparse non-Hermitian positive definite system of linear equations based on the Hermitian and skew-Hermitian splitting (HSS) of the coefficient matrix. A class of (inexact) splitting iteration methods based on HSS and Krylov subspace iteration such as conjugate gradient or other efficient iterations is presented. Convergence analysis of the methods is investigated. Numerical examples are presented to illustrate the effectivness and the advantages of the proposed methods.

Reviewer: Iulian Coroian (Baia Mare)

MSC:

65F10

Iterative numerical methods for linear systems

Keywords:

non-Hermitian matrix; splitting; Hermitian matrix; skew-Hermitian matrix; iterative methods; positive definite system; Krylov subspace iteration; conjugate gradient; convergence; numerical examples