On positivity of principal minors of bivariate Bezier collocation matrix

被引：3
|
作者：
Jaklic, Gasper [1 ,2 ,3 ]
Kanduc, Tadej [4 ]
机构：
[1] Univ Ljubljana, FMF, Ljubljana, Slovenia
[2] Univ Ljubljana, IMFM, Ljubljana, Slovenia
[3] Univ Primorska, PINT, Ljubljana, Slovenia
[4] Turboinst Dd, Ljubljana, Slovenia
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 227卷
关键词：
Collocation matrix; Principal minor; Bivariate Bernstein polynomial; Positivity; DETERMINANT;
D O I：
10.1016/j.amc.2013.11.034
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is well known that the bivariate polynomial interpolation problem at uniformly distributed domain points of a triangle is correct. Thus the corresponding interpolation matrix M is nonsingular. Schumaker stated the conjecture that all principal submatrices of M are nonsingular too. Furthermore, all of the corresponding determinants (the principal minors) are conjectured to be positive. This result would solve the constrained interpolation problem. In this paper, the conjecture on minors for polynomial degree <= 17 and conjecture for some particular configurations of domain points are confirmed. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码：320 / 328
页数：9
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