GPBi-CG: Generalized Product-type Methods Based on Bi-CG for Solving Nonsymmetric Linear Systems

Authors:
Shao-Liang Zhang
Affiliations:
-
Venue:
SIAM Journal on Scientific Computing
Year:
1997

Citing 0
Cited 17

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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.