TITLE:
Flexible GPBi-CG Method for Nonsymmetric Linear Systems
AUTHORS:
Jia-Min Wang, Tong-Xiang Gu
KEYWORDS:
Krylov Subspace Method; Flexible Preconditioning; Inner-Outer Iteration; GPBi-CG
JOURNAL NAME:
Applied Mathematics,
Vol.3 No.4,
April
27,
2012
ABSTRACT: We present a flexible version of GPBi-CG algorithm which allows for the use of a different preconditioner at each step of the algorithm. In particular, a result of the flexibility of the variable preconditioner is to use any iterative method. For example, the standard GPBi-CG algorithm itself can be used as a preconditioner, as can other Krylov subspace methods or splitting methods. Numerical experiments are conducted for flexible GPBi-CG for a few matrices including some nonsymmetric matrices. These experiments illustrate the convergence and robustness of the flexible iterative method.