关于矩阵值Pad型逼近的注记

NOTES ON MATRIX VALUED Padé TYPE APPROXIMANTS

引入了矩阵的行向量列展开概念，利用向量值Ｐａｄé型逼近的有关结论，给出了矩阵Ｐａｄé型逼近的新定义及其相关的重要性质，讨论了矩阵Ｎｅｗｔｏｎ—Ｐａｄé型逼近的问题，证明了唯一性定理，并给出了误差估计。

In this paper,the concept of row vectors expanded by columns is introduced.By using the results of vector valued Padé type approximants,the new definition and the corresponding important propertiesof matrix valued Padé type approximants are described. An example given in the paper shows that the Padé type approximant has better approximating effect at the poles of the function than the Padé approximant. The problems about matrix Newton Padé type approximants are discussed,the uniqueness theorem is proved,and a useful error formula is given.