Interval Branch and Bound Algorithm for Finding the First-Zero-Crossing-Point in One-Dimensional Functions

Interval Branch and Bound Algorithm for Finding the First-Zero-Crossing-Point in One-Dimensional... In this paper, new ideas have been incorporated to a basic interval branch-and-bound algorithm which solves the problem of finding zeros in one-dimensional functions. These new ideas are based on the combination of a new rejection criterion, a selection strategy and an easy-to-obtain precondition of the problem at hand. The methodology described here focuses on finding the first zero crossing point, allowing the search of other zero crossing points to be avoided. In addition, a heuristic subdivision criterion has been proposed that, compared to bisection rule, provides improvements in most of the forty problems that have been tested. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Interval Branch and Bound Algorithm for Finding the First-Zero-Crossing-Point in One-Dimensional Functions

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2000 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:1009917222929
Publisher site
See Article on Publisher Site

Abstract

In this paper, new ideas have been incorporated to a basic interval branch-and-bound algorithm which solves the problem of finding zeros in one-dimensional functions. These new ideas are based on the combination of a new rejection criterion, a selection strategy and an easy-to-obtain precondition of the problem at hand. The methodology described here focuses on finding the first zero crossing point, allowing the search of other zero crossing points to be avoided. In addition, a heuristic subdivision criterion has been proposed that, compared to bisection rule, provides improvements in most of the forty problems that have been tested.

Journal

Reliable ComputingSpringer Journals

Published: Oct 7, 2004

References

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