酉延拓矩阵的奇异值分解及其广义逆  

Singular value decomposition and Moore-penrose inverse for unitary extended matrix

作　　者：蔺小林[1] 王震[2] 蒋耀林[1] 

机构地区：[1]西安交通大学理学院信息与系统科学研究所,陕西西安710049 [2]陕西科技大学理学院,陕西西安710021

出　　处：《纯粹数学与应用数学》2008年第1期49-53,共5页Pure and Applied Mathematics

基　　金：国家自然科学基金(NSFC10171080;60472003)

摘　　要：从普通奇异值分解出发，导出了酉延拓矩阵的奇异值和奇异向量与母矩阵的奇异值和奇异向量间的定量关系，同时对酉延拓矩阵的满秩分解及g逆，反射g逆，最小二乘g逆，最小范数g逆作了定量分析，得到了酉延拓矩阵的满秩分解矩阵F，和G，与母矩阵A的分解矩阵F和G之间的关系．最后给出了相应的快速求解算法，并举例说明该算法大大降低了分解的计算量和存储量，提高了计算效率．Based on the ordinary SVD, a quantitative correspondence of the singular values and singular vectors between the unitary extended matrix and its mother matrix is derived. At the same time, we analysis the quantitative correspondence of F^＊and G^＊matrices of unitary extended matrices and its mother matrix A, and the Moore-Penrose inverse, e.g. g-inverse, reflected g-inverse, least square g-inverse, least norm g-inverse. Finally, we also give the corresponding algorithms of SVD and maximum rank decomposition for unitary extended matrix and illustrate the applications above theory. Based on, we can save dramatically the CPU time and memory.

关 键 词：酉延拓矩阵 奇异值分解 满秩分解 MOORE-PENROSE逆 

分 类 号：TN911.7[电子电信—通信与信息系统]