A LANCZOS-ALGORITHM FOR COMPUTING SINGULAR-VALUES AND VECTORS OF LARGE MATRICES

作     者：CULLUM, J WILLOUGHBY, RA LAKE, M 

出 版 物：《SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING》 (工业与应用数学会科学计算杂志)

年 卷 期：1983年第4卷第2期

页      面：197-215页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：singular value decomposition Lanczos bidiagonalization algorithm large matrix 

摘      要：Any real matrix A has associated with it the real symmetric matrix \[ B \equiv \left(\begin{array}{*{20}c} 0 \\ {A^T } \\ \end{array} \begin{array}{*{20}c} A \\ 0 \\ \end{array} \right) \] whose positive eigenvalues are the nonzero singular values of A. Using B and our Lanczos algorithms for computing eigenvalues and eigenvectors of very large real symmetric matrices, we obtain an algorithm for computing singular values and singular vectors of large sparse real matrices. This algorithm provides a means for computing the largest and the smallest or even all of the distinct singular values of many matrices