Properly posed sets of nodes for multivariate lagrange interpolation in Cs

被引：12
|
作者：
Liang, XZ [1 ]
Lü, CM
Feng, RZ
机构：
[1] Jilin Univ, Inst Math, Changchun 130023, Peoples R China
[2] Univ Wisconsin, Ctr Math Sci, Madison, WI 53715 USA
[3] Changchun Coll Taxat, Dept Informat, Changchun 130021, Peoples R China
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2001年 / 39卷 / 02期
关键词：
Lagrange interpolation; multivariate polynomial; properly posed sets of nodes for interpolation; ideal and variety; algebraic hypersurface;
D O I：
10.1137/S0036142999361566
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we apply techniques from the theory of ideals and varieties in algebraic geometry to study the geometric structure of a properly posed set of nodes (or PPSN, for short) for multivariate Lagrange interpolation along an algebraic hypersurface. We provide a hyperplane-superposition process to construct the PPSN for interpolation along an algebraic hypersurface, and as a result, we offer a clear understanding of the geometric structure of the PPSN for multivariate Lagrange interpolation in C-s.
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页码：587 / 595
页数：9
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