求置换因子循环矩阵的逆阵及广义逆阵的快速算法  

THE FAST ALGORITHMS FOR FINDING THE INVERSES AND GENERALIZED INVERSES OF PERMUTATION FACTOR CIRCULANT MATRICES

作　　者：江兆林[1] 刘三阳[1] 张圣贵[1] 

机构地区：[1]西安电子科技大学应用数学系

出　　处：《高等学校计算数学学报》2003年第3期227-234,共8页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(69972036);山东省中青年学术骨干基金

摘　　要：1引言 循环矩阵由于其应用非常广泛而成为一类重要的特殊矩阵,如在图象处理、编码理论、自回归滤波器设计等领域中经常会遇到以这类矩阵为系数的线性系统的求解问题.In this paper, a fast algorithm for calculating the inverse and group inverse and Moore-Penrose inverse of a permutation factor circulant matrix is presented by the fast algorithm for finding polynomials. There is only error of approximation when the fast algorithm is realized by computers, and only the elements in the first row of the permutation factor circulant matrix is used by the fast algorithm, so the result of the computation is accurate in theory. It is a notable character of the algorithm that the singularity of a permutation factor circulant matrix need not be known firstly.

关 键 词：置换因子循环矩阵 逆阵 广义逆阵 快速算法 复数 群逆 MOORE-PENROSE逆 

分 类 号：O241.6[理学—计算数学]