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Title
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Validated evaluation of special mathematical functions
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Author
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Abstract
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| Because of the importance of special functions, several books and a large collection of papers have been devoted to their use and computation, the most well-known being the Abramowitz and Stegun handbook (Abramowitz and Stegun, 1964) [1] and its successor (Olver et al. 0000) [2]. However, until now no environment offers routines for the provable correct multiprecision and radix-independent evaluation of these special functions. We point out how we make good use of series and limit-periodic continued fraction representations in a package that is being developed at the University of Antwerp. Our scalable precision technique is mainly based on the use of sharpened a priori truncation and round-off error upper bounds for real arguments. The implementation is validated in the sense that it returns a sharp interval enclosure for the requested function evaluation, at the same cost as the evaluation. (C) 2013 Elsevier B.V. All rights reserved. |
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Language
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English
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Source (journal)
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Science of computer programming. - Amsterdam
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Publication
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Amsterdam
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2014
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ISSN
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0167-6423
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DOI
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10.1016/J.SCICO.2013.05.006
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Volume/pages
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90
:A
(2014)
, p. 2-20
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ISI
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000338387700002
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Full text (Publisher's DOI)
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Full text (publisher's version - intranet only)
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