The block Lanczos method for linear systems with multiple right-hand sides

Authors:
A. El Guennouni;K. Jbilou;H. Sadok
Affiliations:
Laboratoire d'analyse numérique et d'Optimisation, UFR IIEA-M3, Université des sciences et technologies de Lille, F-59650 Villeneuve d'Ascq, France;Université du Littoral, zone universitaire de la Mi-voix, batiment H. Poincaré, 50 rue F. Buisson, BP 699, F-62228 Calais cedex, France;Université du Littoral, zone universitaire de la Mi-voix, batiment H. Poincaré, 50 rue F. Buisson, BP 699, F-62228 Calais cedex, France
Venue:
Applied Numerical Mathematics
Year:
2004

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Abstract

In the present paper, we present the block Lanczos method for solving linear systems with multiple right-hand sides. We define the method by using matrix-valued orthogonal polynomials and the Schur complement. As for the one right-hand side Lanczos method, the use of matrix-valued orthogonal polynomials will allow us to derive new block Lanczos-type methods such as block Lanczos/Orthodir and block BIODIR algorithms.