NDLI: Accelerated PMHSS iteration methods for complex symmetric linear systems

Content Provider	Springer Nature Link
Author	Zheng, Qing Qing Ma, Chang Feng
Copyright Year	2016
Abstract	In this paper, we introduce and analyze an accelerated preconditioning modification of the Hermitian and skew-Hermitian splitting (APMHSS) iteration method for solving a broad class of complex symmetric linear systems. This accelerated PMHSS algorithm involves two iteration parameters α,β and two preconditioned matrices whose special choices can recover the known PMHSS (preconditioned modification of the Hermitian and skew-Hermitian splitting) iteration method which includes the MHSS method, as well as yield new ones. The convergence theory of this class of APMHSS iteration methods is established under suitable conditions. Each iteration of this method requires the solution of two linear systems with real symmetric positive definite coefficient matrices. Theoretical analyses show that the upper bound σ $_{1}$(α,β) of the asymptotic convergence rate of the APMHSS method is smaller than that of the PMHSS iteration method. This implies that the APMHSS method may converge faster than the PMHSS method. Numerical experiments on a few model problems are presented to illustrate the theoretical results and examine the numerical effectiveness of the new method.
Ending Page	516
Page Count	16
Starting Page	501
File Format	PDF
ISSN	10171398
e-ISSN	15729265
Journal	Numerical Algorithms
Issue Number	2
Volume Number	73
Language	English
Publisher	Springer US
Publisher Date	2016-02-04
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Accelerated technology Algorithms Algebra Iterative methods for linear systems Convergence theory Numerical Analysis Numeric Computing Complex symmetric linear system PMHSS iteration Theory of Computation Iterative methods Sparse matrices
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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