Author(s)

Jia-Min Wang, Tong-Xiang Gu

Graduate School of Chinese Academy of Engineering Physics, Beijing, China.
Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, China.

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.

Krylov Subspace Method; Flexible Preconditioning; Inner-Outer Iteration; GPBi-CG

J. Wang and T. Gu, "Flexible GPBi-CG Method for Nonsymmetric Linear Systems," Applied Mathematics, Vol. 3 No. 4, 2012, pp. 331-335. doi: 10.4236/am.2012.34050.