求鳞状因子循环矩阵的逆阵及广义逆阵的快速算法  

The Fast Algorithms for Computing the Inverses and Generalized Inverses of Scaled Factor Circulant Matrices

作　　者：江兆林[1] 刘三阳[1] 

机构地区：[1]西安电子科技大学应用数学系

出　　处：《工程数学学报》2003年第4期49-53,共5页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金资助项目(69972036);山东省中青年学术骨干资助基金.

摘　　要：利用多项式快速算法,给出了求鳞状因子循环矩阵的逆阵、自反g 逆、群逆及Moore Penrose逆的快速算法。该算法避免了一般快速算法中,要计算大量的三角函数等可能带来误差及影响效率的问题。该算法仅用到鳞状因子循环矩阵的第一行元素及对角阵D中的常数d1,d2,…,dn进行计算,在计算机上实现时只有舍入误差。特别地,在有理数域上用计算机求得的结果是精确的。A fast algorithm for calculating the inverse and selfreflective ginverse and group inverse and MoorePenrose inverse of a scaled factor circulant matrix is presented by the fast algorithm for computing polynomials. The fast algorithm avoids the problems of error and efficiency produced by computing a great number of triangular functions by means of other general fast algorithms. There is only error of approximation when the fast algorithms. There is only error of approximation when the fast algorithm is realized by computers, and only the elements in the first row of the scaled factor circulant matrix and the constants d1,d2,…,dn in the diagonal matrix D are used by the fast algorithm. Specially, the result computed by a computer is accurate over the rational number field.

关 键 词：鳞状因子循环矩阵 逆阵 自反g-逆 群逆 MOORE-PENROSE逆 快速算法 

分 类 号：O151.21[理学—数学]