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On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matricesConjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.
Document ID
19890016283
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Freund, Roland
(Wuerzburg Univ. Germany, F.R. , United States)
Date Acquired
September 6, 2013
Publication Date
December 1, 1988
Subject Category
Numerical Analysis
Report/Patent Number
NASA-CR-185424
RIACS-TR-88.44
NAS 1.26:185424
Accession Number
89N25654
Funding Number(s)
CONTRACT_GRANT: NSF DCR-84-12314
CONTRACT_GRANT: NCC2-387
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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