TY - JOUR
T1 - A Product Hybrid GMRES Algorithm for Nonsymmetric Linear Systems
AU - Bao-Jiang Zhong
JO - Journal of Computational Mathematics
VL - 1
SP - 83
EP - 92
PY - 2005
DA - 2005/02
SN - 23
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8798.html
KW - Nonsymmetric linear systems, Iterative methods, GMRES, Hybrid, Harmonic Ritz values, Residual polynomials.
AB - <p style="text-align: justify;">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.</p>