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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 the numerical computation of these functions, the most well-known being the Abramowitz and Stegun handbook [1]. But up to this date, no environment offers routines for the provable correct evaluation of these special functions. We point out how series and limit-periodic continued fraction representations of the functions can be helpful in this respect. Our scalable precision technique is mainly based on the use of sharpened a priori truncation and round-off error upper bounds, in case of 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. |
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Language
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English
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Source (book)
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Intelligent computer mathematics: proceedings of the 9th International Conference on Artificial Intelligence and Symbolic Computation, July 28-August 1, 2008, Birmingham, England / Autexier, S. [edit.]; et al. [edit.]
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Publication
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Berlin
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Springer
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2008
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ISBN
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978-3-540-85109-7
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Volume/pages
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p. 206-216
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ISI
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000258392600016
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