Paper Info
Title
GPBi-CG: Generalized Product-type Methods Based on Bi-CG for Solving Nonsymmetric Linear Systems
Abstract
Recently Bi-CGSTAB as a variant of Bi-CG has been proposed for solving nonsymmetric linear systems, and its attractive convergence behavior has been confirmed in many numerical experiments. Bi-CGSTAB can be characterized by its residual polynomial which consists of the product of the residual polynomial of Bi-CG with other polynomials generated from two-term recurrence relations. In this paper, we propose a unified way to generalize a class of product-type methods whose residual polynomials can be factored by the residual polynomial of Bi-CG and other polynomials with standard three-term recurrence relations. Such product-type methods which are based on Bi-CG can be regarded as generalizations of Bi-CGSTAB. From the unified way, the well-known variants of the product-type methods, like CGS, Bi-CGSTAB, Bi-CGSTAB2, are reacquired again.
Year
DOI
Venue
1997
10.1137/S1064827592236313
SIAM Journal on Scientific Computing
Keywords
Field
DocType
Bi-CG,Bi-CGSTAB,Bi-CGSTAB2,CGS,nonsymmetric linear systems,product-type methods,restructuring Bi-CG,residual polynomial,three-term recurrence relations
Convergence (routing),Residual,Mathematical optimization,Polynomial,Algebra,Linear system,Mathematical analysis,Recurrence relation,Generalization,Product type,Mathematics
Journal
Volume
Issue
ISSN
18
2
1064-8275
Citations 
PageRank 
References 
36
4.14
0
Authors
1
Name
Order
Citations
PageRank
Shao-Liang Zhang19219.06