Title
Validated evaluation of special mathematical functions Validated evaluation of special mathematical functions
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
conferenceObject
Publication
Berlin :Springer, [*]
Subject
Mathematics
Computer. Automation
Source (book)
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.]
ISBN - Hoofdstuk
978-3-540-85109-7
ISI
000258392600016
Carrier
E
Target language
English (eng)
Affiliation
University of Antwerp
Abstract
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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