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GMRESR: A family of nested GMRES methods. (English) Zbl 0839.65040

Summary: T. Eirola and O. Nevanlinna [Linear Algebra Appl. 121, 511-520 (1989; Zbl 0683.65018)] have proposed an iterative solution method for unsymmetric linear systems, in which the preconditioner is updated from step to step. Following their ideas we suggest variants of the generalized minimal residual (GMRES) method, in which a preconditioner is constructed per iteration step by a suitable approximation process, e.g., by GMRES itself. Our numerical experiments indicate that this may lead to considerable savings in CPU-time and memory requirements in typical CFD applications.

MSC:

65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling

Citations:

Zbl 0683.65018

Software:

CGS; LSQR
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Full Text: DOI

References:

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