NDLI: Accurate and Fast Evaluation of Elementary Symmetric Functions

Content Provider	IEEE Xplore Digital Library
Author	Hao Jiang Graillat, S. Barrio, R.
Copyright Year	2013
Description	Author affiliation: Dipt. de Mat. Aplic., Univ. de Zaragoza, Zaragoza, Spain (Barrio, R.) \|\| Sch. of Sci., Nat. Univ. of Defense Technol., Changsha, China (Hao Jiang) \|\| PEQUAN, Univ. Pierre et Marie Curie, Paris, France (Graillat, S.)
Abstract	This paper is concerned with the fast and accurate evaluation of elementary symmetric functions. We present a new compensated algorithm by applying error-free transformations to improve the accuracy of the so-called Summation Algorithm, which is used, by example, in the MATLAB's poly function. We derive a forward round off error bound and running error bound for our new algorithm. The round off error bound implies that the computed result is as accurate as if computed with twice the working precision and then rounded to the current working precision. The running error analysis provides a shaper bound along with the result, without increasing significantly the computational cost. Numerical experiments illustrate that our algorithm runs much faster than the algorithm using the classic double-double library while sharing similar error estimates. Such an algorithm can be widely applicable for example to compute characteristic polynomials from eigen values. It can also be used into the Rasch model in psychological measurement.
Sponsorship	IEEE Comput. Soc.
Starting Page	183
Ending Page	190
File Size	283820
Page Count	8
File Format	PDF
ISBN	9781467356442
ISSN	10636889
DOI	10.1109/ARITH.2013.18
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-04-07
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Algorithm design and analysis Accuracy Polynomials Vectors Roundoff errors Libraries accurate algorithm elementary symmetric functions floating-point arithmetic roundoff error error-free transformation compensated algorithm
Content Type	Text
Resource Type	Article

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