Stability of GPBiCG_AR Method Based on Minimization of Associate Residual

Authors:
Moe Thuthu;Seiji Fujino
Affiliations:
Graduate School of Information Science and Electrical Engineering,;Research Institute for Information Technology, Kyushu University, Japan
Venue:
Computer Mathematics
Year:
2008

Citing 3
Cited 1

BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems

SIAM Journal on Scientific and Statistical Computing
GPBi-CG: Generalized Product-type Methods Based on Bi-CG for Solving Nonsymmetric Linear Systems

SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems

Accurate fluid-structure interaction computations using elements without mid-side nodes

Computational Mechanics

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Abstract

GPBi-CG method is an attractive iterative method for the solution of a linear system of equations with nonsymmetric coefficient matrix. However, the popularity of GPBi-CG method has diminished over time except for the minority. In this paper, we consider a new algorithm based on minimization of the associate residual of 2-norm in place of reconstruction of the algorithm. We refer to a method with new algorithm as GPBiCG with Associate Residual (abbreviated as GPBiCG_AR) method. Moreover we will introduce preconditioned GPBiCG_AR (abbreviated as P_GPBiCG_AR). Then, we will support that GPBiCG_AR and P_GPBiCG_AR methods yield safety convergence through numerical experiments.