矩阵有理逼近

Matrix Valued Rational Approximation

中文关键词:  矩阵  连分式  逼近

英文关键词:matrix  continued fraction  approximation.

中文摘要:

      本文利用Ｓａｍｅｌｓｏｎ逆变换得到了方阵逆阵的一个新方法，以此建立了Ｔｈｉｅｌｅ型矩阵连分式的展开式，将Ｔｈｉｅｌｅ定理推广到矩阵上去．首次引入了矩阵有理逼近的概念，并讨论和证明了它的特征性和唯一性．最后，给出了逼近式的余项公式．

英文摘要:

      In this paper, the Samelson inverse is used to obtain a new method of matrix inverse,then the expansion of T hiele type matrix valued continued froctions is constructed via an efficient coefficient algorithm. Thiele theorem is generalized to the matrix case. The concept of matrix valued rational approximation is introduced, its characteriration and uniqueness are discussed and proven. Finally, a useful remainder formula of the approxdriation expression is given.