Abstract. Let q⩾1 be an integer, S q be the unit sphere embedded in R q+1 , and μq be the volume element of S q . For x 0 ∈ S q , and α∈(0,π), let S α q ( x 0 ) ...
In this paper, we prove the existence of quadrature formulas with nonnegative weights that are exact for evaluating integrals of polynomials of a fixed degree ...
Oct 22, 2024 · We consider sequences Q(m(n)), n is an element of N, of cubature (or numerical integration) rules, where Q(m(n)) is assumed to integrate exactly ...
Introduction. Many applications involving function approximation on the sphere require an approximate evaluation of an integral over a subset of the sphere.
Let <i>q</i> ≥ 1 be an integer, S<sup><i>q</i></sup> be the unit sphere embedded in R<sup><i>q</i>+1</sup>, and µ<inf><i>q</i></inf> be the volume element ...
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Let q ≥ 1 be an integer, K be a compact subset of the unit sphere S embedded in the Euclidean space IR, and K have a nonempty interior relative to S. Let C ...
In this paper, we present an algorithm for computing quadrature formulas based on “scattered data” on a triangle; i.e., without re- quiring a theoretically ...
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The purpose of this paper is to construct universal, auto-adaptive, localized, linear, polynomial (-valued) operators based on scattered data on the (hyper) ...
Oct 22, 2024 · An important ingredient of this analysis is to develop numerical integration schemes (quadrature formulas) to integrate spherical polynomials of ...
The discretisation of the unit sphere using a product of one-dimensional quadra- ture points is likely to be the most trivial extension of standard quadrature ...
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