Title
Validated computation of certain hypergeometric functions Validated computation of certain hypergeometric functions
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
New York, N.Y. ,
Subject
Mathematics
Computer. Automation
Source (journal)
ACM transactions on mathematical software. - New York, N.Y.
Volume/pages
38(2011) :2 , p. 11,1-11,20
ISSN
0098-3500
Article Reference
11
Carrier
E-only publicatie
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
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.
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