Cubature formulas for symmetric measures in higher dimensions with few points期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Cubature formulas for symmetric measures in higher dimensions with few points

Authors:	Aicke Hinrichs Erich Novak

Affiliation:	Mathematisches Institut, Universität Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany ; Mathematisches Institut, Universität Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany

Abstract:	We study cubature formulas for -dimensional integrals with an arbitrary symmetric weight function of product form. We present a construction that yields a high polynomial exactness: for fixed degree $\ell=5$ or $\ell=7$ and large dimension the number of knots is only slightly larger than the lower bound of Möller and much smaller compared to the known constructions. We also show, for any odd degree $\ell = 2k+1$ , that the minimal number of points is almost independent of the weight function. This is also true for the integration over the (Euclidean) sphere.

Keywords:	Cubature formulas M\"oller bound Smolyak method polynomial exactness

	点击此处可从《Mathematics of Computation》浏览原始摘要信息
	点击此处可从《Mathematics of Computation》下载全文