On Convergence Bounds of GMRES Algorithm

摘要：

In this paper we first make a brief review of GMRES convergence results. Then we derive new bounds for the GMRES residual norm by making use of a unitary matrix U and a Hermitian positive definite matrix P which are GMRES-equivalent to the cofficient matrix A with respect to the initial residual r0. The existence of such U and P was proved by Leonid2. As a GMRES residual norm bound for linear systems with Hermitian positive definite cofficient matrices is known and a GMRES residual norm bound for linear systems with unitary cofficient matrices can be readily derived from Liesens work1, our new bounds follow from the fact that two GMRES-equivalent matrices make the same residual.

作者: Gang Xie

作者单位: Institute of Computer Applications, CAEP, China

会议类型: 国际会议

会议名称: Proceedings of The Fourth International Conference on Parallel and Distribyted Computing,Applications and Technologies(第四届并行与分布式计算应用与技术国际会议)

会议地点: 成都

会议语种:英文

页码: 750-753

在线出版日期: 2003-08-27（万方平台首次上网日期，不代表论文的发表时间）