Volume 20, pp. 119-138, 2005.

Oblique projection methods for linear systems with multiple right-hand sides

K. Jbilou, H. Sadok, and A. Tinzefte

Abstract

In the present paper, we describe new Lanczos-based methods for solving nonsymmetric linear systems of equations with multiple right-hand sides. These methods are based on global oblique projections of the initial residual onto a matrix Krylov subspace. We first derive the global Lanczos process to construct biorthonormal bases and we give some of its properties. Then we introduce new methods such as the global BCG and the global BiCGSTAB algorithms. Look-ahead versions of these algorithms are also given. Finally numerical examples will be given.

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Key words

Global Lanczos, matrix Krylov subspace, block methods, iterative methods, nonsymmetric linear systems, multiple right-hand sides

AMS subject classifications

65F10, 65F25

Links to the cited ETNA articles

[6]	Vol. 16 (2003), pp. 129-142 A. El Guennouni, K. Jbilou, and H. Sadok: A block version of BiCGSTAB for linear systems with multiple right-hand sides

ETNA articles which cite this article

Vol. 51 (2019), pp. 495-511 A. Badahmane, A. H. Bentbib, and H. Sadok: Preconditioned global Krylov subspace methods for solving saddle point problems with multiple right-hand sides

Vol. 58 (2023), pp. 348-377 Alessandro Buccini, Lucas Onisk, and Lothar Reichel: Range restricted iterative methods for linear discrete ill-posed problems

Vol. 58 (2023), pp. 470-485 F. Bouyghf, A. Messaoudi, and H. Sadok: An enhancement of the convergence of the IDR method

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