Volume 33, pp. 207-220, 2008-2009.

Algebraic properties of the block GMRES and block Arnoldi methods

L. Elbouyahyaoui, A. Messaoudi, and H. Sadok


The solution of linear systems of equations with several right-hand sides is considered. Approximate solutions are conveniently computed by block GMRES methods. We describe and study three variants of block GMRES. These methods are based on three implementations of the block Arnoldi method, which differ in their choice of inner product.

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Key words

block method, GMRES method, Arnoldi method, matrix polynomial, multiple right-hand sides, block Krylov subspace, Schur complement, characteristic polynomial.

AMS subject classifications


ETNA articles which cite this article

Vol. 46 (2017), pp. 162-189 Kirk M. Soodhalter: Stagnation of block GMRES and its relationship to block FOM
Vol. 46 (2017), pp. 215-232 Moritz August, Mari Carmen Bañuls, and Thomas Huckle: On the approximation of functionals of very large Hermitian matrices represented as matrix product operators
Vol. 47 (2017), pp. 18-36 L. Elbouyahyaoui, M. Heyouni, K. Jbilou, and A. Messaoudi: A block Arnoldi based method for the solution of the Sylvester-observer equation
Vol. 47 (2017), pp. 100-126 Andreas Frommer, Kathryn Lund, and Daniel B. Szyld: Block Krylov subspace methods for functions of matrices

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