High-precision numerical integration: progress and challenges

Title: High-precision numerical integration: progress and challenges
Creator: Bailey, D. H.; Borwein, J. M.
Relation: Journal of Symbolic Computation Vol. 46, Issue 7, p. 741-754
Publisher Link: http://dx.doi.org/10.1016/j.jsc.2010.08.010
Publisher: Academic Press
Resource Type: journal article
Date: 2011
Description: One of the most fruitful advances in the field of experimental mathematics has been the development of practical methods for very high-precision numerical integration, a quest initiated by Keith Geddes and other researchers in the 1980s and 1990s. These techniques, when coupled with equally powerful integer relation detection methods, have resulted in the analytic evaluation of many integrals that previously were beyond the realm of symbolic techniques. This paper presents a survey of the current state-of-the-art in this area (including results by the present authors and others), mentions some new results, and then sketches what challenges lie ahead.
Subject: quadrature; numerical integration; high precision arithmetic; quantum field theory; Ising theory
Identifier: http://hdl.handle.net/1959.13/1038229
Identifier: uon:13523
Identifier: ISSN:0747-7171
Language: eng
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