o-对称矩阵的奇异值分解及其算法

SINGULAR VALUE DECOMPOSITION AND ALGORITHM OF o-SYMMETRIC MATRIX

本文研究了具有轴对称结构矩阵的奇异值分解,找出了这类矩阵奇异值分解与其子阵奇异值分解之间的定量关系.利用这些定量关系给出这类矩阵奇异值分解和Moore-Penrose逆的算法,据此可极大地节省求该类矩阵奇异值分解和Moore-Penrose逆时的计算量和存储量.

This paper studies singular value decomposition of axial symmetric matrix, and the quantitative correspondence of the singular value decomposition of axial symmetric matrix to its submatrix is given. At the same time, the author gives algorithm of singular value decomposition and Moore-Penrose inverses of axial symmetric matrix,which saves dramatically the CPU time and memory when calculate the singular value decomposition and Moore-Penrose inverses for the axial symmetric matrix.