摘要
1.引言
在科学工程计算中经常需要计算大规模矩阵的少数最大或最小的奇异值及其所对应的奇异子空间.
This paper concerns the computation of a few large (or small) singular values and the associated singular vectors of an l×n matrix A. They are the square roots of the large (or the small) eigenvalues and the eigenvectors of the cross-product matrix AT A. So instead of solving the full SVD problem we solve the eigenproblem of the cross-product matrix using projection methods, and then revert it to the original one. For the cross-product matrix ATA, an explicitly restarted refined Lanczos algorithm and an implicitly restarted refined Lanczos algorithm are proposed. A convergence analysis is presented for the Ritz value, Ritz vector and refined Ritz vector. Numerical experiments show that two refined algorithms are far superior to their conventional counterparts.
出处
《计算数学》
CSCD
北大核心
2003年第3期293-304,共12页
Mathematica Numerica Sinica
基金
国家重点基础研究专项基金(G19990328)
高等学校骨干教师基金资助项目
