求解大型稀疏线性方程组的加权拟极小残差算法  

A weighted quasi-minimal residual algorithm for large sparse system of linear equations

作　　者：陈晓花 CHEN Xiao-hua(Longqiao College of Lanzhou University of Finance and Economics,Lanzhou 730101,China)

机构地区：[1]兰州财经大学陇桥学院,甘肃兰州730101

出　　处：《青海师范大学学报（自然科学版）》2021年第2期30-35,共6页Journal of Qinghai Normal University(Natural Science Edition)

摘　　要：拟极小残差算法(QMR)是基于Lanczos双正交化过程的求解大型稀疏线性方程组的一种Krylov子空间方法.为了加快其收敛速度,采用加权技术,将QMR算法中的普通Euclidean内积用D-内积来代替,构造得到加权Lanczos双D-正交化算法,在此基础上得到加权拟极小残差算法(WQMR).数值算例表明,对某些矩阵特别是带状矩阵,该算法的收敛性优于QMR算法.The Quasi-minimal residual algorithm(QMR)is a Krylov subspace method for solving large sparse linear equations based on Lanczos biorthogonalization.In order to accelerate the convergence speed,the weighted Euclidean inner product in the QMR algorithm was replaced by the D-inner product,and the weighted Lanczos d-orthogonalization algorithm was constructed.On this basis,the weighted quasi-Minimal residual algorithm(WQMR)was obtained.Numerical examples show that the convergence of this algorithm is better than that of QMR algorithm for some matrices,especially for banded matrices.

关 键 词：线性方程组 拟极小残差算法 KRYLOV子空间方法 

分 类 号：O241.6[理学—计算数学]