Can a minimal degree 6 cubature rule for the disk have all points inside?

被引：3

作者：

Easwaran, C

Fialkow, L

Petrovic, S ^{[1
]}

机构：

[1] Western Michigan Univ, Dept Math, Kalamazoo, MI 49008 USA

[2] SUNY Albany, Dept Comp Sci, New Paltz, NY 12561 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2006年 / 185卷 / 01期

关键词：

cubature rules; positive moment matrix; flat extensions;

D O I：

10.1016/j.cam.2005.02.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We use positivity and extension properties of moment matrices to prove that a 10-node (minimal) cubature rule of degree 6 for planar measure on the closed unit disk 6 cannot have all nodes in D. We construct examples showing that such rules may have as many as 9 points in D, and we provide similar examples for the triangle. (c) 2005 Elsevier B.V. All rights reserved.

引用

页码：144 / 165

页数：22