A device for reduction of computational cost applicable to a family of IDR(s) methods(Algorithms for Matrix/Eigenvalue Problems and their Applications,<Special Issue>Joint Symposium of JSIAM Activity Groups 2009)

Abstract

IDR(s), Bi_IDR(s) and GIDR(s, L) methods based on the IDR Theorem have been proposed one after another. It is crucial how to build up a dense matrix P in view of reduction of computational cost and maintenance of convergence rate in a family of IDR(s) methods. Therefore, in this paper, we propose a device for building up a dense matrix P which is applicable commonly to a family of IDR(s) methods. Through numerical experiments, we clarify that the strategy of the proposed a Slim Dense matrix P is very effective for improvement of efficiency of IDR(s), Bi_IDR(s) and GIDR(s, L) methods.