多元矩阵值切触有理插值

J4 ›› 2010, Vol. 48 ›› Issue (03): 353-360.

多元矩阵值切触有理插值

陈少田, 夏朋, 郭岩, 张树功

吉林大学数学研究所, 长春 130012

收稿日期:2009-09-16 出版日期:2010-05-26 发布日期:2010-05-19
通讯作者: 张树功 E-mail:sgzh@mail.jlu.edu.cn

Multivariate Matrix Valued Osculatory Rational |Interpolation

CHEN Shaotian, XIA Peng, GUO Yan, ZHANG Shugong

Institute of Mathematics, Jilin University, Changchun 130012, China

Received:2009-09-16 Online:2010-05-26 Published:2010-05-19
Contact: ZHANG Shugong E-mail:sgzh@mail.jlu.edu.cn

摘要/Abstract

摘要：

将矩阵值切触有理插值问题转化为求R-模的Groebner基问题, 并用递推算法计算模的Groebner基. 利用这个Groebner基, 可以得到包含
多元矩阵值有理插值问题所有可能弱解(P(X),q(X))的参数化形式. 针对具体应用, 可以通过选择恰当的参数获取所需的矩阵值有理插值解.

关键词: 矩阵值切触有理插值, 弱插值, 模的Groebner基

Abstract:

The task of seeking the weak solution (P(X),q(X)) of matrix valued osculatory rational interpolation was converted into
computing the Groebner bases of R-submodule M of the free module over the polynomial ring. This Groebner bases can be computed recursively to obtain a parametric rational interpolation function with the Groebner bases. Choosing these parameters properly, we may get the desired matrix valued rational interpolation function.

Key words: matrix valued osculatory rational interpolation, weak interpolation, Groebner base for module

中图分类号:

O241.3

陈少田, 夏朋, 郭岩, 张树功. 多元矩阵值切触有理插值[J]. J4, 2010, 48(03): 353-360.

CHEN Shao-Tian, JIA Peng, GUO Yan, ZHANG Shu-Gong. Multivariate Matrix Valued Osculatory Rational |Interpolation[J]. J4, 2010, 48(03): 353-360.