内积空间上向量值Padé-型逼近表的块状结构特征

上海大学学报(自然科学版) ›› 2010, Vol. 16 ›› Issue (3): 253-256.

内积空间上向量值Padé-型逼近表的块状结构特征

苏瑞,潘宝珍

(上海大学理学院,上海 200444)

出版日期:2010-06-28 发布日期:2010-06-28

Block Structure of Vector-Valued Padé-Type Table in the Inner Space

SU Rui,PAN Bao-zhen

（College of Sciences, Shanghai University, Shanghai 200444, China）

Online:2010-06-28 Published:2010-06-28

摘要/Abstract

摘要：

从多项式空间到向量空间引入一种广义线性泛函,在内积空间上定义和构造向量值Padé-型逼近.借助向量值Padé型逼近的误差公式,给出关于线性泛函的正交多项式的定义,同时推导出向量值Padé-型逼近表的块状结构特征.利用Padé型逼近表的这一特征,可以减少向量值Padé-型逼近的计算量.最后,通过数值实例说明该方法的有效性.

关键词: 向量值；Padé-型逼近；正交多项式；块状结构特征

Abstract:

A vector-valued Padé-type approximation is defined in the inner space by introducing a generalized linear functional from a polynomial space to a vector space. With the error formula for vector-valued Padé-type approximation, the orthogonal polynomial with respect to a generalized linear functional is defined. The block structure of Padé-type table is derived. The structure can be used to reduce computation of Padé-type approximations. An example is given to illustrate effectiveness of the method.

Key words: vector-valued; Padé-type approximation; orthogonal polynomial; block structure

苏瑞,潘宝珍. 内积空间上向量值Padé-型逼近表的块状结构特征[J]. 上海大学学报(自然科学版), 2010, 16(3): 253-256.

SU Rui,PAN Bao-zhen. Block Structure of Vector-Valued Padé-Type Table in the Inner Space[J]. Journal of Shanghai University（Natural Science Edition）, 2010, 16(3): 253-256.