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A composite step bi-conjugate gradient algorithm for nonsymmetric linear systems. (English) Zbl 0809.65025
The composite step bi-conjugate gradient (CSBCG) algorithm, which is a useful modification of the BCG algorithm, is derived. The CSBCG algorithm eliminates pivot break-downs, assuming that the underlying Lanczos process does not break-down. The BCG algorithm and the break-down possibilities are briefly reviewed. It is proved that CSBCG is able to compute exactly those BCG iterates that are well-defined. The choice of some heuristic strategies for deciding when to take a composite step as well as details of implementation are discussed thoroughly. Numerical experiments are given.

65F10Iterative methods for linear systems
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