矩阵广义奇异值分解的一种算法  

Computing the Generalized Singular Value Decompositions

作　　者：徐兰[1] 王守根[1] 

机构地区：[1]华东师范大学数学系

出　　处：《华东师范大学学报（自然科学版）》1989年第2期17-26,共10页Journal of East China Normal University(Natural Science)

摘　　要：本文论述了一种A的B奇异值分解的算法。算法分为二大部分,首先是对矩阵(A B)进行列主元QR团式分解,将这个广义奇异值分解问题归结为具有正交列的分块矩阵(Q_1 Q_3)的CS分解问题,其次就是给出关于(Q_1 Q_2)的CS分解的计算方法,这个算法避免了中的重正交化和中对子矩阵的再一次SVD计算,在一定条件下它是快速的且稳定。A stable and fast scheme is described to compute the generalized singular value decomposition (GSVD) of a matrix pair (A, B). The new algorithm not only avoid the cross product matrix but also is more faster than Van Loan's. Our main steps are that matrices A and B are reduced to upper bidiagonal forms at the same time and an iterative mathod for computing GSVD is constructed. At the first step, the modified algorithm is poposed to avoid the failure of the reduction caused by small elements.Numerical experiment is presented and the amount of multiplication is valued.

关 键 词：双对角阵 奇异值分解 广义 计算法 

分 类 号：O241.6[理学—计算数学]