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High-precision numerical integration: progress and challenges. (English) Zbl 1291.65070

Summary: 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.

MSC:

65D30 Numerical integration
65Y05 Parallel numerical computation
68W30 Symbolic computation and algebraic computation

Software:

ARPREC; MPI
PDFBibTeX XMLCite
Full Text: DOI

References:

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