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The rate of convergence of sparse grid quadrature on the torus

Hegland, Markus; Leopardi, Paul

Description

We examine sparse grid quadrature on Korobov spaces; that is, weighted tensor product reproducing kernel Hilbert spaces on the torus. We describe a dimension adaptive quadrature algorithm based on an algorithm of Hegland [ANZIAM J., 44(E):C335, 2003], and also formulate a version of Wasilkowski and Wozniakowski's weighted tensor product algorithm [J. Complexity, 15(3):402, 1999]. We claim that our algorithm is generally lower in cost than Wasilkowski and Wozniakowski's algorithm, and therefore...[Show more]

CollectionsANU Research Publications
Date published: 2011
Type: Journal article
URI: http://hdl.handle.net/1885/21750
Source: ANZIAM Journal

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