Interval Mathematical Library Based on Chebyshev and Taylor Series Expansion

Interval Mathematical Library Based on Chebyshev and Taylor Series Expansion In this paper, we present a mathematical library designed for use in interval solvers of nonlinear systems of equations. The library computes the validated upper and lower bounds of ranges of values of elementary mathematical functions on an interval, which are optimal in most cases. Computation of elementary functions is based on their expansion in Chebyshev and Taylor series and uses the rounded directions setting mechanism. Some original techniques developed by the authors are applied in order to provide high speed and accuracy of the computation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Interval Mathematical Library Based on Chebyshev and Taylor Series Expansion

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Publisher
Kluwer Academic Publishers-Plenum Publishers
Copyright
Copyright © 2005 by Springer Science + Business Media, Inc.
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1007/s11155-005-0042-3
Publisher site
See Article on Publisher Site

Abstract

In this paper, we present a mathematical library designed for use in interval solvers of nonlinear systems of equations. The library computes the validated upper and lower bounds of ranges of values of elementary mathematical functions on an interval, which are optimal in most cases. Computation of elementary functions is based on their expansion in Chebyshev and Taylor series and uses the rounded directions setting mechanism. Some original techniques developed by the authors are applied in order to provide high speed and accuracy of the computation.

Journal

Reliable ComputingSpringer Journals

Published: Jan 1, 2005

References

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