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 flow. In this article a floating point 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.
M. Sofroniou, G. Spaletta (2005). Precise Numerical Computation. JOURNAL OF LOGIC AND ALGEBRAIC PROGRAMMING, 64, Issue 1, 113-134 [10.1016/j.jlap.2004.07.007].
Precise Numerical Computation
SPALETTA, GIULIA
2005
Abstract
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 flow. In this article a floating point 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
