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.

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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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