Volume 30, pp. 1-9, 2008.

Simpler Block GMRES for nonsymmetric systems with multiple right-hand sides

Hualei Liu and Baojiang Zhong


A Simpler Block GMRES algorithm is presented, which is a block version of Walker and Zhou's Simpler GMRES. Similar to Block GMRES, the new algorithm also minimizes the residual norm in a block Krylov space at every step. Theoretical analysis shows that the matrix-valued polynomials constructed by the new algorithm is the same as the original one. However, Simpler Block GMRES avoids the factorization of a block upper Hessenberg matrix. In consequence, it is much simpler to program and requires less work. Numerical experiments are conducted to illustrate the performance of the new block algorithm.

Full Text (PDF) [192 KB], BibTeX

Key words

linear systems, iterative methods, block methods, GMRES, Simpler GMRES

AMS subject classifications


ETNA articles which cite this article

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

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