High-Precision Computation: Mathematical Physics and Dynamics

Bailey, D. H. ; Barrio, R. ; Borwein, J. M.

Lawrence Berkeley National Laboratory

关键词: Body;    Conversion;    Uses;    Physics;    Scattering Amplitudes;   

DOI  :  10.2172/983781
RP-ID  :  LBNL-3534E
RP-ID  :  DE-AC02-05CH11231
RP-ID  :  983781

美国|英语

来源: UNT Digital Library

【 摘 要 】

At the present time, IEEE 64-bit oating-point arithmetic is suficiently accurate for most scientic applications. However, for a rapidly growing body of important scientic computing applications, a higher level of numeric precision is required. Such calculations are facilitated by high-precision software packages that include high-level language translation modules to minimize the conversion e ort. This pa- per presents a survey of recent applications of these techniques and provides someanalysis of their numerical requirements. These applications include supernova simulations, climate modeling, planetary orbit calculations, Coulomb n-body atomic systems, studies of the one structure constant, scattering amplitudes of quarks, glu- ons and bosons, nonlinear oscillator theory, experimental mathematics, evaluation of orthogonal polynomials, numerical integration of ODEs, computation of periodic orbits, studies of the splitting of separatrices, detection of strange nonchaotic at- tractors, Ising theory, quantum held theory, and discrete dynamical systems. We conclude that high-precision arithmetic facilities are now an indispensable compo- nent of a modern large-scale scientic computing environment.