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Abstract : |
Abstract. It is well-known that Bi-CG can be adapted so that the operations with A T can be avoided, and hybrid methods can be constructed in which it is attempted to further improve the convergence behaviour. Examples of this are CGS, Bi-CGSTAB, and the more general BiCGstab(`) method. In this paper it is shown that BiCGstab(`) can be implemented in different ways. Each of the suggested approaches has its own advantages and disadvantages. Our implementations allow for combinations of Bi-CG with arbitrary polynomial methods. The choice for a specific implementation can also be made for reasons of numerical stability. This aspect receives much attention. Various effects have been illustrated by numerical examples. Key words. Bi-Conjugate gradients, non-symmetric linear systems, CGS, Bi-CGSTAB, iterative, |
