Validated computation of certain hypergeometric functions-Reference-Cited by-同舟云学术

Validated computation of certain hypergeometric functions

Published:2011-12 Issue:2 Volume:38 Page:1-20
ISSN:0098-3500
Container-title:ACM Transactions on Mathematical Software
language:en
Short-container-title:ACM Trans. Math. Softw.

Author:

Colman Michel¹,Cuyt Annie¹,Deun Joris Van¹

Affiliation:

1. Universiteit Antwerpen, Belgium

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.

Publisher

Association for Computing Machinery (ACM)

Subject

Applied Mathematics,Software

Link

https://dl.acm.org/doi/pdf/10.1145/2049673.2049675

Reference19 articles.

1. Backeljauw F. 2009. A library for radix-independent multiprecision IEEE-compliant floating-point arithmetic. Tech. rep. 2009-01 Department of Mathematics and Computer Science Universiteit Antwerpen. Backeljauw F. 2009. A library for radix-independent multiprecision IEEE-compliant floating-point arithmetic. Tech. rep. 2009-01 Department of Mathematics and Computer Science Universiteit Antwerpen.

2. Backeljauw F. Becuwe S. Cuyt A. and Van Deun J. 2009. Validated evaluation of special mathematical functions. Tech. rep. 2009--04 Department of Mathematics and Computer Science Universiteit Antwerpen. Backeljauw F. Becuwe S. Cuyt A. and Van Deun J. 2009. Validated evaluation of special mathematical functions. Tech. rep. 2009--04 Department of Mathematics and Computer Science Universiteit Antwerpen.

3. Cuyt A. Petersen V. B. Verdonk B. Waadeland H. and Jones W. B. 2008. Handbook of Continued Fractions for Special Functions. Springer New York. Cuyt A. Petersen V. B. Verdonk B. Waadeland H. and Jones W. B. 2008. Handbook of Continued Fractions for Special Functions. Springer New York.

4. Efficient and Reliable Multiprecision Implementation of Elementary and Special Functions

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