The Accuracy Of Floating Point Summation (1993)
| Venue: | SIAM J. Sci. Comput |
| Citations: | 32 - 0 self |
BibTeX
@ARTICLE{Higham93theaccuracy,
author = {Nicholas J. Higham},
title = {The Accuracy Of Floating Point Summation},
journal = {SIAM J. Sci. Comput},
year = {1993},
volume = {14},
pages = {783--799}
}
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Abstract
. The usual recursive summation technique is just one of several ways of computing the sum of n floating point numbers. Five summation methods and their variations are analysed here. The accuracy of the methods is compared using rounding error analysis and numerical experiments. Four of the methods are shown to be special cases of a general class of methods, and an error analysis is given for this class. No one method is uniformly more accurate than the others, but some guidelines are given on the choice of method in particular cases. Key words. floating point summation, rounding error analysis, orderings. AMS subject classifications. primary 65G05, secondary 65B10. 1. Introduction. Sums of floating point numbers are ubiquitous in scientific computing. They occur when evaluating inner products, means, variances, norms, and all kinds of nonlinear functions. Although, at first sight, summation might appear to offer little scope for algorithmic ingenuity, the usual "recursive summation...
