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On SSOR‐like preconditioners for non‐Hermitian positive definite matrices
Author(s) -
Bai ZhongZhi
Publication year - 2016
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2004
Subject(s) - generalized minimal residual method , krylov subspace , hermitian matrix , mathematics , positive definite matrix , eigenvalues and eigenvectors , linear system , preconditioner , coefficient matrix , convergence (economics) , matrix (chemical analysis) , mathematical analysis , pure mathematics , physics , materials science , quantum mechanics , economics , composite material , economic growth
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.