Minimal cubature rules and polynomial interpolation in two variables II

被引：5

作者：

Xu, Yuan ^{[1
]}

机构：

[1] Univ Oregon, Dept Math, Eugene, OR 97403 USA

来源：

JOURNAL OF APPROXIMATION THEORY | 2017年 / 214卷

关键词：

Cubature; Minimal cubature; Polynomial interpolation; Two variables; Lebesgue constant; ORTHOGONAL POLYNOMIALS; FORMULAS;

D O I：

10.1016/j.jat.2016.11.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

As a complement to Xu (2012), minimal cubature rules of degree 4m + 1 for the weight functions W-alpha,W-beta +/- 1/2 (x , y) = vertical bar x + y vertical bar(2 alpha+1) vertical bar x - y vertical bar(2 beta+1)((1 - x(2))(1 - y(2)))(+/- 1/2) on [-1, 1](2) are shown to exist and near minimal cubature rules of the same degree with one node more than minimal are constructed explicitly. The Lagrange interpolation polynomials on the nodes of the near minimal cubature rules are also studied. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：49 / 68

页数：20

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