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Precise numerical computation

Mark Sofroniou
Organization: Wolfram Research, Inc.
Department: Kernel Technology
G. Spaletta
Organization: Bologna University
Department: Mathematics Dept
Journal / Anthology

Journal of Logic and Algebraic Programming
Year: 2005
Volume: 64
Issue: 1
Page range: 113-134

Arithmetic systems such as those based on IEEE standards currently make no attempt to track the propagation of errors. A formal error analysis, however, can be complicated and is often confined to the realm of experts in numerical analysis. In recent years, there has been a resurgence of interest in automated methods for accurately monitoring the error propagation. In this article, a floatingpoint system based on significance arithmetic will be described. Details of the implementation in Mathematica will be given along with examples that illustrate the design goals and differences over conventional fixed-precision floating-point systems.

*Applied Mathematics > Numerical Methods
*Wolfram Technology > Kernel > Numerics