Paper Info
Title
Accelerated PMHSS iteration methods for complex symmetric linear systems.
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 ź,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 ź1(ź,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.
Year
DOI
Venue
2016
10.1007/s11075-016-0105-z
Numerical Algorithms
Keywords
Field
DocType
Complex symmetric linear system,PMHSS iteration,Convergence theory,Iterative methods,Accelerated technology,65F10,65F50
Mathematical optimization,Linear system,Preconditioner,Mathematical analysis,Matrix (mathematics),Iterative method,Upper and lower bounds,Positive-definite matrix,Rate of convergence,Hermitian matrix,Mathematics
Journal
Volume
Issue
ISSN
73
2
1017-1398
Citations 
PageRank 
References 
7
0.45
17
Authors
2
Name
Order
Citations
PageRank
Qingqing Zheng1171.00
Changfeng Ma219729.63