K. Abe and S.-L. Zhang, “A Variable Preconditioning Using The SOR Method For GCR-like Methods,” International Journal of Numerical Analysis and Modeling, Vol. 2, No.2, 2005, pp. 147-161.

has been cited by the following article:

• 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.