Publication
Title
Validated computation of certain hypergeometric functions
Author
Abstract
We present an efficient algorithm for the validated high-precision computation of real continued fractions, accurate to the last digit. The algorithm proceeds in two stages. In the first stage, computations are done in double precision. A forward error analysis and some heuristics are used to obtain an a priori error estimate. This estimate is used in the second stage to compute the fraction to the requested accuracy in high precision (adaptively incrementing the precision for reasons of efficiency). A running error analysis and techniques from interval arithmetic are used to validate the result. As an application, we use this algorithm to compute Gauss and confluent hypergeometric functions when one of the numerator parameters is a positive integer.
Language
English
Source (journal)
ACM transactions on mathematical software. - New York, N.Y.
Publication
New York, N.Y. : 2011
ISSN
0098-3500
Volume/pages
38:2(2011), p. 11,1-11,20
Article Reference
11
ISI
000298638200002
Medium
E-only publicatie
Full text (Publisher's DOI)
UAntwerpen
Faculty/Department
Research group
[E?say:metaLocaldata.cgzprojectinf]
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 05.03.2012
Last edited 16.08.2017
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