BiCGStab(l) for families of shifted linear systems

Authors:
A. Frommer
Affiliations:
Fachbereich Mathematik, Bergische Universität Wuppertal, D-42097 Wuppertal, Germany
Venue:
Computing
Year:
2003

Citing 6
Cited 3

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Abstract

We consider a seed system Ax = b together with a shifted linear system of the form (A + σI)x = b, σ ∈ C, A ∈ Cn×n, b ∈ Cn. We develop modifications of the BiCGStab(l) method which allow to solve the seed and the shifted system at the expense of just the matrix-vector multiplications needed to solve Ax = b via BiCGStab(l). On the shifted system, these modifications do not perform the corresponding BiCGStab(l)-method, but we show, that in the case that A is positive real and σ ≥ 0, the resulting method is still a well-smoothed variant of BiCG. Numerical examples from an application arising in quantum chromodynamics are given to illustrate the efficiency of the method developed.