線型連立系に対する積型反復解法の加速多項式の評価

概要

論文の詳細を見る
CG, Bi-CG methods are well-known iterative solutions of linear equation : Ax=b. CGS, Bi-CGSTAB, GPBi-CG methods have been developed as faster modifications for Bi-CG. The residual of interative methods, involving CGS, Bi-CGSTABand GPBi-CG, is represented with a product of the residual of Bi-CG method and the matrix polynomial which accelerates the convergence of the Bi-CG method. We call such iterative methods product-type, while the polynomial is said to be the accelerating polynomial. It has been recognized that the methods are useful to many practical applications. They are, however, easily influenced by rounding errors. In this paper, we analyze the effects of the accelerating polynomial on rounding errors for the product-type methods through numerical experiments. The present paper is hopefully a guideline for practical use of a the product-type methods.
日本応用数理学会の論文
1996-12-15