摘要
对每个复对称矩阵AT＝A∈Cn×n，理论上已证，存在一个酉矩阵U，使A＝UT∑U（1），其中∑为非负对角阵，式（1）称为A的对称奇异值分解（SSVD），本文提出一种求复对称矩陈SSVD的Jacobi型方法。
If AT = A = B + iD∈Cn×n,then there is a unitary matrix U such that A = UT∑U,the SSVD of A, where ∑ is nonnegative diagonal. In the paper, a Jacobi - type schemeScheme 1 for the SSVD is proposed. The SSVD of A is equivalent to a SVD of a 2n - by - 2n real matrix . One Jacobi - type scheme - Scheme 2 can be used to solve the One Jacobi - type scheme - Scheme 2 can be used to solve the SVD of M. The convergence properties of Scheme 1 and 2 are discussed. Numerical examples show that the computed results of Scheme 1 and Scheme 2 often have the same accuracy, but Scheme 2 requires much more machine time than Scheme 1.
出处
《华东师范大学学报（自然科学版）》
CAS
CSCD
北大核心
1998年第2期1-6,共6页
Journal of East China Normal University(Natural Science)
