Hesse, Kerstin and Womersley, Robert S (2012) Numerical integration with polynomial exactness over a spherical cap. Advances in Computational Mathematics, 36 (3). pp. 451-483. ISSN 1019-7168

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Abstract

This paper presents rules for numerical integration over spherical caps and discusses their properties. For a spherical cap on the unit sphere S2 , we discuss tensor product rules with n 2/2 + O(n) nodes in the cap, positive weights, which are exact for all spherical polynomials of degree ≤ n, and can be easily and inexpensively implemented. Numerical tests illustrate the performance of these rules. A similar derivation establishes the existence of equal weight rules with degree of polynomial exactness n and O(n 3) nodes for numerical integration over spherical caps on S2 . For arbitrary d ≥ 2, this strategy is extended to provide rules for numerical integration over spherical caps on Sd that have O(n d ) nodes in the cap, positive weights, and are exact for all spherical polynomials of degree ≤ n. We also show that positive weight rules for numerical integration over spherical caps on Sd that are exact for all spherical polynomials of degree ≤ n have at least O(n d ) nodes and possess a certain regularity property

Item Type:	Article
Schools and Departments:	School of Mathematical and Physical Sciences > Mathematics
Depositing User:	Kerstin Hesse
Date Deposited:	31 Jan 2013 14:50
Last Modified:	31 Jan 2013 14:50
URI:	http://sro.sussex.ac.uk/id/eprint/17111

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