High-Precision Computation: Mathematical Physics and Dynamics
Dr Jonathan Borwein, CARMA
MSI Access Grid SeminarDATE: 2010-06-02
TIME: 14:00:00 - 15:00:00
LOCATION: Baume Theatre (Room 1.04) in Peter Baume Building
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ABSTRACT:
At the present time, IEEE 64-bit floating-point 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 high- precision software packages that include high-level language translation modules to minimize the conversion effort. This talk and associated 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 $n$-body 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 strange nonchaotic attractors, Ising theory, quantum field theory, and discrete dynamical systems. We conclude that high-precision arithmetic facilities are now an indispensable component of a modern large- scale scientific computing environment.
This is joint work with D. Bailey (Lawrence Berkeley) and R. Barrio
(Zaragoza). The paper is available at
http://www.carma.newcastle.edu.au/~jb616/hpmd.pdf
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