An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices Part II
نویسنده
چکیده
In Part I [6] of this paper, we have presented an implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices. Here, we show how the look-ahead Lanczos process | combined with a quasi-minimal residual (QMR) approach | can be used to develop a robust black box solver for large sparse non-Hermitian linear systems. Details of an implementation of the resulting QMR algorithm are presented. It is demonstrated that the QMR method is closely related to the biconjugate gradient (BCG) algorithm; however, unlike BCG, the QMR algorithm has smooth convergence curves and good numerical properties. In particular, BCG iterates can be recovered stably from the QMR process. We report numerical experiments with our implementation of the look-ahead Lanczos algorithm, both for eigenvalue problems and linear systems. Also, program listings of FORTRAN implementations of the look-ahead Lanczos algorithm and the QMR method are included.
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