Quadrature formulas for integration of multivariate trigonometric polynomials on spherical triangles

被引：5
|
作者：
Beckmann, J. [1 ]
Mhaskar, H. N. [2 ,3 ]
Prestin, J. [1 ]
机构：
[1] Univ Lubeck, Inst Math, Ratzeburger Allee 160, D-23562 Lubeck, Germany
[2] Calif State Univ Los Angeles, Dept Math, Los Angeles, CA 90032 USA
[3] CALTECH, Pasadena, CA 91125 USA
来源：
GEM-INTERNATIONAL JOURNAL ON GEOMATHEMATICS | 2012年 / 3卷 / 01期
基金：
美国国家科学基金会;
关键词：
Quadrature formulas; Spherical triangles; Gautschi algorithm;
D O I：
10.1007/s13137-012-0035-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We describe an explicit construction of quadrature rules exact for integrating multivariate trigonometric polynomials of a given coordinatewise degree on a spherical triangle. The theory is presented in the more general setting of quadrature formulas on a compact subset of the unit hypersphere, S-q, embedded in the Euclidean space Rq+1. The number of points at which the polynomials are sampled is commensurate with the dimension of the polynomial space.
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页码：119 / 138
页数：20
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