利用矩阵乘积的LU分解计算广义逆
Computing generalized inverses using LU factorization of matrix product
摘要：
给出了一个计算有理矩阵A的{2，3}，{2，4}，{1，2，3}，{1，2，4} -逆和Moore-Penrose逆的算法.类A（2，3）s和A（2，4）s用矩阵乘积（R*A）+R* 和T*（AT*）+来刻画，其中R和T是具有适当维数和相应秩的有理矩阵.该算法是基于这些一般表示和对称正定矩阵的Cholesky分解。该算法用程序设计语言MATHEMATICA和DELPHI实现，并通过实例加以说明。该算法的数值结果，对应的Moore-Penrose逆，与相应的结果进行了比较，通过几个已知的方法计算的Moore-Penrose逆。
英文摘要：
An algorithm for computing {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4} -inverses and the Moore-Penrose inverse of a given rational matrix A is established. Classes A(2, 3)s and A(2, 4)s are characterized in terms of matrix products (R*A)+R* and T*(AT*)+, where R and T are rational matrices with appropriate dimensions and corresponding rank. The proposed algorithm is based on these general representations and the Cholesky factorization of symmetric positive matrices. The algorithm is implemented in programming languages MATHEMATICA and DELPHI, and illustrated via examples. Numerical results of the algorithm, corresponding to the Moore-Penrose inverse, are compared with corresponding results obtained by several known methods for computing the Moore-Penrose inverse.
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