Transpose-free Lanczos-type algorithms for nonsymmetric linear systems |
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Authors: | Brezinski C. Redivo-Zaglia M. |
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Affiliation: | (1) Laboratoire d'Analyse Numérique et d'Optimisation, Université des Sciences et Technologies de Lille, F-59655 Villeneuve d'Ascq Cedex, France E-mail:;(2) Dipartimento di Elettronica e Informatica, Università degli Studi di Padova, Via Gradenigo 6/a, I-35131 Padova, Italy |
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Abstract: | The method of Lanczos for solving systems of linear equations is implemented by using recurrence relationships between formal orthogonal polynomials. A drawback is that the computation of the coefficients of these recurrence relationships usually requires the use of the transpose of the matrix of the system. Due to the indirect addressing, this is a costly operation. In this paper, a new procedure for computing these coefficients is proposed. It is based on the recursive computation of the products of polynomials appearing in their expressions and it does not involve the transpose of the matrix. Moreover, our approach allows to implement simultaneously and at a low price a Lanczos-type product method such as the CGS or the BiCGSTAB. This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | Lanczos' method orthogonal polynomials CGS BiCGSTAB 65F10 33A65 |
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