摘要
A large unsymmetric linear system problem is transformed into the problem of computing the eigenvector of a large symmetric nonnegative definite matrix associated with the eigenvalue zero, i.e., the computation of the elgenvector of the cross-product matrix of an augmented matrix associated with the eigenvalue zero. The standard Lanczos method and an improved refined Lanczos method are proposed that compute approximate eigenvectors and return approximate solutions of the linear system. An implicitly restarted Lanczos algorithm and its refined version are developed. Theoretical analysis and numerical experiments show the refined method is better than the standard one. If the large matrix has small eigenvalues, the two new algorithms are much faster than the unpreconditioned restarted GMRES.
A large unsymmetric linear system problem is transformed into the problem of computing the eigenvector of a large symmetric nonnegative definite matrix associated with the eigenvalue zero, i.e., the computation of the eigenvector of the cross-product matrix of an augmented matrix associated with the eigenvalue zero. The standard Lanczos method and an improved refined Lanczos method are proposed that compute approximate eigenvectors and return approximate solutions of the linear system. An implicitly restarted Lanczos algorithm and its refined version are developed. Theoretical analysis and numerical experiments show the refined method is better than the standard one. If the large matrix has small eigenvalues, the two new algorithms are much faster than the unpreconditioned restarted GMRES.
出处
《数值计算与计算机应用》
CSCD
北大核心
2004年第1期48-59,共12页
Journal on Numerical Methods and Computer Applications
基金
国家重点基础研究专项基金(G1999032805)
关键词
非对称线性方程组
Lanczos法
增广矩阵
奇异向量
特征值
数值计算
orthogonal projection, refined projection, Ritz value, Ritz vector, refined vector, Lanczos method, implicit restart
