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Symbolic-numeric integration of rational functions.

Authors :
Moir, Robert H. C.
Corless, Robert M.
Maza, Marc Moreno
Xie, Ning
Source :
Numerical Algorithms; Apr2020, Vol. 83 Issue 4, p1295-1320, 26p
Publication Year :
2020

Abstract

We consider the problem of symbolic-numeric integration of symbolic functions, focusing on rational functions. Using a hybrid method allows the reliable yet efficient computation of symbolic antiderivatives while avoiding issues of ill-conditioning to which numerical methods are susceptible. We propose two alternative methods for exact input that compute the rational part of the integral using Hermite reduction and then compute the transcendental part two different ways using a combination of exact integration and efficient numerical computation of roots. The symbolic computation is done within bpas, or Basic Polynomial Algebra Subprograms, which is a highly optimized environment for polynomial computation on parallel architectures, while the numerical computation is done using the highly optimized multiprecision rootfinding package MPSolve. We provide for both algorithms computable expressions for the first-order term of a structured forward and backward error and show how, away from singularities, tolerance proportionality is achieved by adjusting the precision of the rootfinding tasks. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10171398
Volume :
83
Issue :
4
Database :
Complementary Index
Journal :
Numerical Algorithms
Publication Type :
Academic Journal
Accession number :
142815444
Full Text :
https://doi.org/10.1007/s11075-019-00726-6