Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6875351 | Science of Computer Programming | 2014 | 19 Pages |
Abstract
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.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Franky Backeljauw, Stefan Becuwe, Annie Cuyt, Joris Van Deun, Daniel W. Lozier,