二元矩阵连分式逼近的对偶展开式(Ⅲ)

A Dual Expansion for Bivariate Matrix Valued Continued Fraction Approximation

本文借助于矩阵的广义逆变换和分支连分式的递推算法，得到了二元Ｔｈｉｅｌｅ型矩阵连分式的对偶展开式，并对对偶展开式的逼近性质进行了讨论．两种互为对偶的连分式逼近之间的一个关联性质得到了证明．

In this paper,by means of the generalized inverse for matrixs and the recursive algorithms for branched continued fractions, a dual expansion for bivariate Thiele-type matrix valued continued fractions is obtained. Some approximation properties are discussed . A inner connection between two continued fraction approximation which are dual to each other is proved . Some examples are given to illustrate the results of the paper.