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Quasi‐HSS iteration methods for non‐Hermitian positive definite linear systems of strong skew‐Hermitian parts
Author(s) -
Bai ZhongZhi
Publication year - 2018
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.2116
Subject(s) - krylov subspace , hermitian matrix , mathematics , arnoldi iteration , linear system , positive definite matrix , generalized minimal residual method , convergence (economics) , matrix (chemical analysis) , power iteration , iterative method , mathematical analysis , algorithm , eigenvalues and eigenvectors , pure mathematics , physics , materials science , quantum mechanics , economics , composite material , economic growth
Summary For large sparse non‐Hermitian positive definite linear systems, we establish exact and inexact quasi‐HSS iteration methods and discuss their convergence properties. Numerical experiments show that both iteration methods are effective and robust when they are used either as linear solvers or as matrix splitting preconditioners for the Krylov subspace iteration methods. In addition, these two iteration methods are, respectively, much more powerful than the exact and inexact HSS iteration methods, especially when the linear systems have nearly singular Hermitian parts or strongly dominant skew‐Hermitian parts, and they can be employed to solve non‐Hermitian indefinite linear systems with only mild indefiniteness.