模上的Groebner基与切触有理插值

模上的Groebner基与切触有理插值

陈少田, 夏朋, 张树功, 金凯

吉林大学数学研究所, 长春 130012

收稿日期:2009-01-15 修回日期:1900-01-01 出版日期:2009-05-26 发布日期:2009-06-23
通讯作者: 张树功

On Multivariate Osculatory Rational Interpolation andGroebner Bases for Modules

CHEN Shaotian, XIA Peng, ZHANG Shugong, JIN Kai

Institute of Mathematics, Jilin University, Changchun 130012, China

Received:2009-01-15 Revised:1900-01-01 Online:2009-05-26 Published:2009-06-23
Contact: ZHANG Shugong

摘要/Abstract

摘要： 利用模上的Groebner基研究多元切触有理插值问题, 得到了多元有理函数a(X)/b(X)的参数化表示, 并给出一种构造多元切触有理插值算法. 当插值问题退化为Cauchy型有理插值问题时, 相应的算法即为多元有理插值的Newton型算法.

关键词: 多元切触有理插值, 弱插值, 模的Groebner基

Abstract: A new algorithm was derived for determining a parameterization of multivariate osculatory rational functions a(X)/b(X) interpolating an arbitrary sequence of points by means of Groebner bases of submodules of the free module over the polynomial ring in multivariate variable. For Cauchy multivariate rational interpolation, the algorithm is a Newton algorithm.

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

中图分类号:

O241.3

陈少田, 夏朋, 张树功, 金凯. 模上的Groebner基与切触有理插值[J]. J4, 2009, 47(03): 502-504.

CHEN Shaotian, XIA Peng, ZHANG Shugong, JIN Kai. On Multivariate Osculatory Rational Interpolation andGroebner Bases for Modules[J]. J4, 2009, 47(03): 502-504.