基于广义逆的矩阵Pad■逼近

1．引言矩阵Pade逼近在变分原理、在原子及初等粒子物理中已有深入的实际应用背景（［1，2］）．由于原有的矩阵Pade逼近都要涉及矩阵的乘法，而矩阵的乘法一般不满足交换律，从而在一定程度上限制了该逼近方法的应用范围．本文给出一种新的基于广义过的矩阵Pade逼近，它与原有的矩阵Pade逼近方法相比具有下列特点：第一．在构造过程中不需用到矩阵的乘法运算，没有左、右Pade逼近的区别，从而拓宽了应用范围（见下面说明），并且蕴含着它在数值分析和实际问题中的应用价值．第二，它可以用两种不同的格式计算出来：（1）分母多项式的显式…

A MATRIX PADE APPROXIMANTS BASED ON GENERALIZED INVERSE

In this paper, a new matrix pade approximants which is based on generalized inverse is obtained. It is different from original matrix pade approximants in that it need not use multiplication of matrixces in its constructive process, hence, lefthanded pade approximants is same as right-handed ones in the cases. Generalized inverse matrix pade approximants can be computed by two methods: (i) the determinantal formula for denoninator polynomials; (ii) matrix -algorithm. The results in the paper are verified by some numerical examples.