求解非对称线性方程组的GMRES法的收敛性

Convergence of GMRES for solving unsymmetric linear systems

对求解大型非对称线性方程组问题，Ｓａａｄ提出了ＧＭＲＥＳ法．在理论方面，Ｓａａｄ仅对系数阵可对角化时给出了收敛性分析．本文将取消这一限制，对系数阵Ａ为亏损的一般情况，建立了该方法的误差估计式。

For unsymmetric linear system, Saad has proposed the GMRES(Generalized Minimal Residual Algorithm). Theoretically, Saad has proved that if A is diagoralizable, GMRES converges. This paper cancels this restriction to A, establishes the error estimate of method and accounts for the convergence of GMRES for any matrix A.