ON A WEIGHTED QUASI-RESIDUAL MINIMIZATION STRATEGY FOR SOLVING COMPLEX SYMMETRIC SHIFTED LINEAR SYSTEMS
Tomohiro Sogabe, Takeo Hoshi, Takeo Fujiwara · arXiv (Cornell University) · 2008
Abstract. We consider the solution of complex symmetric shifted linear systems. Such systems arise in largescale electronic structure simulations, and there is a strong need of algorithms for their fast solution. With the aim of solving the systems efficiently, we consider a special case of the QMR method for non-Hermitian shifted linear systems and propose its weighted quasi-minimal residual approach. A numerical algorithm, referred to as shifted QMR SYM(B), is obtained by the choice of a weight which is particularly cost-effective. Numerical examples are presented to show the performance of the shifted QMR SYM(B) method. Key words. Complex symmetric matrices, shifted linear systems, Krylov methods, COCG, QMR SYM. AMS subject classifications. 65F10. 1. Introduction. In