Volume 16, pp. 129-142, 2003.

A block version of BiCGSTAB for linear systems with multiple right-hand sides

A. El Guennouni, K. Jbilou, and H. Sadok


We present a new block method for solving large nonsymmetric linear systems of equations with multiple right-hand sides. We first give the matrix polynomial interpretation of the classical block biconjugate gradient (Bl-BCG) algorithm using formal matrix-valued orthogonal polynomials. This allows us to derive a block version of BiCGSTAB. Numerical examples and comparisons with other block methods are given to illustrate the effectiveness of the proposed method.

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Key words

block Krylov subspace, block methods, Lanczos method, multiple right-hand sides, nonsymmetric linear systems.

AMS subject classifications


ETNA articles which cite this article

Vol. 20 (2005), pp. 119-138 K. Jbilou, H. Sadok, and A. Tinzefte: Oblique projection methods for linear systems with multiple right-hand sides
Vol. 41 (2014), pp. 478-496 Jing Meng, Pei-Yong Zhu, Hou-Biao Li, and Xian-Ming Gu: A deflated block flexible GMRES-DR method for linear systems with multiple right-hand sides
Vol. 46 (2017), pp. 460-473 M. Addam, M. Heyouni, and H. Sadok: The block Hessenberg process for matrix equations
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. 470-485 F. Bouyghf, A. Messaoudi, and H. Sadok: An enhancement of the convergence of the IDR method

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