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Mathematics 2015, 3(2), 337-367;

High-Precision Arithmetic in Mathematical Physics

Lawrence Berkeley National Laboratory (retired) and University of California, Davis, Davis, CA 95616, USA
CARMA, University of Newcastle, Callaghan, NSW 2308, Australia
Author to whom correspondence should be addressed.
Academic Editor: Palle E.T. Jorgensen
Received: 19 January 2015 / Accepted: 16 April 2015 / Published: 12 May 2015
(This article belongs to the Special Issue Mathematical physics)
Full-Text   |   PDF [904 KB, uploaded 12 May 2015]


For many scientific calculations, particularly those involving empirical data, IEEE 32-bit floating-point arithmetic produces results of sufficient accuracy, while for other applications IEEE 64-bit floating-point is more appropriate. But for some very demanding applications, even higher levels of precision are often required. This article discusses the challenge of high-precision computation, in the context of mathematical physics, and highlights what facilities are required to support future computation, in light of emerging developments in computer architecture. View Full-Text
Keywords: high-precision arithmetic; numerical integration; PSLQ algorithm; Ising integrals; Poisson equation high-precision arithmetic; numerical integration; PSLQ algorithm; Ising integrals; Poisson equation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Bailey, D.H.; Borwein, J.M. High-Precision Arithmetic in Mathematical Physics. Mathematics 2015, 3, 337-367.

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