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HighPrecision Computation and Mathematical Physics
"... At the present time, IEEE 64bit floatingpoint arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing applications, a higher level of numeric precision is required. Such calculations are facilitated by highpreci ..."
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Cited by 11 (3 self)
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At the present time, IEEE 64bit floatingpoint arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing applications, a higher level of numeric precision is required. Such calculations are facilitated by highprecision software packages that include highlevel language translation modules to minimize the conversion effort. This paper presents a survey of recent applications of these techniques and provides some analysis of their numerical requirements. These applications include supernova simulations, climate modeling, planetary orbit calculations, Coulomb nbody atomic systems, scattering amplitudes of quarks, gluons and bosons, nonlinear oscillator theory, Ising theory, quantum field theory and experimental mathematics. We conclude that highprecision arithmetic facilities are now an indispensable component of a modern largescale scientific computing environment.
HighPrecision Arithmetic: Progress and Challenges
"... For many scientific calculations, particularly those involving empirical data, IEEE 32bit floatingpoint arithmetic produces results of sufficient accuracy, while for other applications IEEE 64bit floatingpoint is more appropriate. But for some very demanding applications, even higher levels of p ..."
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Cited by 1 (0 self)
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For many scientific calculations, particularly those involving empirical data, IEEE 32bit floatingpoint arithmetic produces results of sufficient accuracy, while for other applications IEEE 64bit floatingpoint is more appropriate. But for some very demanding applications, even higher levels of precision are often required. This article discusses the challenge of highprecision computation and presents a sample of applications, including some new results from the past year or two. This article also discusses what facilities are required to support future highprecision computing, in light of emerging applications and changes in computer architecture, such as highly parallel systems and graphical processing units.
HighPrecision Computation: Mathematical Physics and Dynamics
, 2010
"... At the present time, IEEE 64bit floatingpoint arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing applications, a higher level of numeric precision is required. Such calculations are facilitated by highprecisi ..."
Abstract
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At the present time, IEEE 64bit floatingpoint arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing applications, a higher level of numeric precision is required. Such calculations are facilitated by highprecision software packages that include highlevel language translation modules to minimize the conversion effort. This paper presents a survey of recent applications of these techniques and provides some analysis of their numerical requirements. These applications include supernova simulations, climate modeling, planetary orbit calculations, Coulomb nbody atomic systems, studies of the fine structure constant, scattering amplitudes of quarks, gluons 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 SNAs, Ising theory, quantum field theory, and discrete dynamical systems. We conclude that highprecision arithmetic facilities are now an indispensable component of a modern largescale scientific computing environment.
1 HighPrecision Arithmetic: Progress and Challenges
"... Abstract—For many scientific calculations, particularly those involving empirical data, IEEE 32bit floatingpoint arithmetic produces results of sufficient accuracy, while for other applications IEEE 64bit floatingpoint is more appropriate. But for some very demanding applications, even higher le ..."
Abstract
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Abstract—For many scientific calculations, particularly those involving empirical data, IEEE 32bit floatingpoint arithmetic produces results of sufficient accuracy, while for other applications IEEE 64bit floatingpoint is more appropriate. But for some very demanding applications, even higher levels of precision are often required. This article discusses the challenge of highprecision computation and presents a sample of applications, including some new results from the past year or two. This article also discusses what facilities are required to support future highprecision computing, in light of emerging applications and changes in computer architecture, such as highly parallel systems and graphical processing units. Index Terms—highprecision arithmetic, numerical analysis, numerical error, experimental mathematics 1