A PRODUCT HYBRID GMRES ALGORITHM FOR NONSYMMETRIC LINEAR SYSTEMS

• 来源期刊: 计算数学(英文版)
• 关键词: Nonsymmetric linear systems Iterative methods GMRES Hybrid Harmonic Ritz values Residual polynomials.
• 年，卷（期）: 2005,（1）
• 页码范围: 83-92
• 页数: 10页
• 语种: 英文

摘要

It has been observed that the residual polynomials resulted from successive restarting cycles of GMRES(m) may differ from one another meaningfully. In this paper, it is further shown that the polynomials can complement one another harmoniously in reducing the iterative residual. This characterization of GMRES(m) is exploited to formulate an efficient hybrid iterative scheme, which can be widely applied to existing hybrid algorithms for solving large nonsymmetric systems of linear equations. In particular, a variant of the hybrid GMRES algorithm of Nachtigal, Reichel and Trefethen (1992) is presented. It is described how the new algorithm may offer significant performance improvements over the original one.