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Validated Evaluation of Special Mathematical Functions

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Intelligent Computer Mathematics (CICM 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5144))

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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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Serge Autexier John Campbell Julio Rubio Volker Sorge Masakazu Suzuki Freek Wiedijk

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© 2008 Springer-Verlag Berlin Heidelberg

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Backeljauw, F., Becuwe, S., Cuyt, A. (2008). Validated Evaluation of Special Mathematical Functions. In: Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M., Wiedijk, F. (eds) Intelligent Computer Mathematics. CICM 2008. Lecture Notes in Computer Science(), vol 5144. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85109-7

  • Online ISBN: 978-3-540-85110-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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