Error Reduction of the Taylor Centered Form by Half and an Inner Estimation of the Range

Error Reduction of the Taylor Centered Form by Half and an Inner Estimation of the Range We show that the overestimation error of the interval Horner method for univariate polynomials on a centered interval is reduced at least by half if the interval is split at its midpoint zero and the interval Horner method is applied to both halves separately. This observation is used to reduce the overestimation error of the Taylor centered form at least by half. Further, it can be used to compute error bounds for the Taylor centered form and an inner range estimation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Error Reduction of the Taylor Centered Form by Half and an Inner Estimation of the Range

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 1997 by Kluwer Academic Publishers
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.
10.1023/A:1009901621378
Publisher site
See Article on Publisher Site

Abstract

We show that the overestimation error of the interval Horner method for univariate polynomials on a centered interval is reduced at least by half if the interval is split at its midpoint zero and the interval Horner method is applied to both halves separately. This observation is used to reduce the overestimation error of the Taylor centered form at least by half. Further, it can be used to compute error bounds for the Taylor centered form and an inner range estimation.

Journal

Reliable ComputingSpringer Journals

Published: Oct 14, 2004

References

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