High-Precision Arithmetic in Mathematical Physics

David H. Bailey and Jonathan M. Borwein
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David H. Bailey: Lawrence Berkeley National Laboratory (retired) and University of California, Davis, Davis, CA 95616, USA
Jonathan M. Borwein: CARMA, University of Newcastle, Callaghan, NSW 2308, Australia

Mathematics, 2015, vol. 3, issue 2, 1-31

Abstract: 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.

Keywords: high-precision arithmetic; numerical integration; PSLQ algorithm; Ising integrals; Poisson equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2015
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