基于Lanczos双A-正交的一种修正的QMR算法

A MODIFIED QMR ALGORITHM BASED ON THE A-LANCZOS BIORTHOGONAL PROCESS

本文研究了基于Lanczos双正交过程的拟极小残量法(QMR).将QMR算法中的Lanczos双正交过程用Lanczos双A-正交过程代替,利用该算法得到的近似解与最后一个基向量的线性组合来作为新的近似解,使新近似解的残差范数满足一个一维极小化问题,从而得到一种基于Lanczos双A-正交的修正的QMR算法.数值试验表明,对于某些大型线性稀疏方程组,新算法比QMR算法收敛快得多.

The quasi minimum residual method（QMR） based on the Lanczos bi-orthogonal process was studied in this paper.A-Lanczos bi-orthogonal process was introduced to replace the Lanczos bi-orthogonal process.Using the linear combination of the approximate solution and the lasted basis vectoris as a new approximate solution of the algorithm,the residual norm of new approximate solution can satisfy a one-dimensional minimization problem,so as to get a modified QMR algorithm based on the A-Lanczos bi-orthogonal process.The numerical experiments showed that the new algorithm converges faster than the original QMR algorithm for some large sparse linear systems.