High-precision computation: Mathematical physics and dynamics

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• 作者：D.H. Baileyup>aup>up> ; up>up>1up>up> ; up>up>dhbailey@lbl.govup> ; R. Barrioup>bup>up> ; up>up>2up>up> ; up>up>rbarrio@unizar.esup> ; J.M. Borweinup>cup>up> ; up>up>3up>up> ; up>up>jonathan.borwein@newcastle.edu.auup>
• 关键词：High-precision computation ; Mathematical physics ; Dynamical systems ; Experimental mathematics
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：15 June, 2012
• 卷：218
• 期：20
• 页码：10106-10121
• 文件大小：1396 K

摘要

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 paper presents an overview of recent applications of these techniques and provides some analysis of their numerical requirements. We conclude that high-precision arithmetic facilities are now an indispensable component of a modern large-scale scientific computing environment.