The IBiCGStab method for large and sparse unsymmetric linear systems

206. L. T. Yang and R. P. Brent, The improved BiCGStab method for large and sparse unsymmetric linear systems on parallel distributed memory architectures, Proceedings of the Fifth International Conference on Algorithms and Architectures for Parallel Processing (ICA3PP-02), Beijing, October 2002, 324-328.

Paper: pdf (135K).


In this paper, an improved version (IBiCGStab) of the BiCGStab method of van der Vorst [SIAM J. Sci. Statist. Computing 13 (1992), 631-644] for the solution of large and sparse linear systems of equations with unsymmetric coefficient matrices is proposed. The method combines elements of numerical stability and parallel algorithm design without increasing the computational cost. The algorithm is derived so that all inner products of a single iteration step are independent and the communication time required for inner products can be overlapped efficiently with the computation time of vector updates. The efficiency of the method is demonstrated by numerical experiments carried out on a massively parallel distributed memory system.

[For a longer abstract, see the paper.]


A related paper is [203].

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