On SSOR‐like preconditioners for non‐Hermitian positive definite matrices. Issue 1 (14th July 2015)

• Record Type: Journal Article
• Authors: Bai, Zhong‐Zhi
• Is Part Of: Numerical linear algebra with applications. Volume 23:Issue 1(2016:Jan.)
• Page Start: 37
• Page End: 60
• Publication Date: 2015-07-14
• Subjects: non‐Hermitian matrix -- positive definiteness -- preconditioning -- SSOR iteration -- eigenvalue distribution; Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.2004
• Languages: English
• ISSNs: 1070-5325

Abstract

SUMMARY: We construct, analyze, and implement SSOR‐like preconditioners for non‐Hermitian positive definite system of linear equations when its coefficient matrix possesses either a dominant Hermitian part or a dominant skew‐Hermitian part. We derive tight bounds for eigenvalues of the preconditioned matrices and obtain convergence rates of the corresponding SSOR‐like iteration methods as well as the corresponding preconditioned GMRES iteration methods. Numerical implementations show that Krylov subspace iteration methods such as GMRES, when accelerated by the SSOR‐like preconditioners, are efficient solvers for these classes of non‐Hermitian positive definite linear systems. Copyright © 2015 John Wiley & Sons, Ltd.