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
article
Publication
Amsterdam ,
Subject
Computer. Automation
Source (journal)
Science of computer programming. - Amsterdam
Volume/pages
90(2014) :A , p. 2-20
ISSN
0167-6423
ISI
000338387700002
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
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. (C) 2013 Elsevier B.V. All rights reserved.
E-info
https://repository.uantwerpen.be/docman/iruaauth/d86328/4717996.pdf
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000338387700002&DestLinkType=RelatedRecords&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000338387700002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000338387700002&DestLinkType=CitingArticles&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848
Handle