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AN ALGORITHM FOR FINDING ALL ZEROS OF VECTOR FUNCTIONS

Part of: Nonlinear algebraic or transcendental equations Computer aspects of numerical algorithms

Published online by Cambridge University Press:  01 June 2008

IBRAHEEM ALOLYAN
IBRAHEEM ALOLYAN*
Affiliation:
Mathematics Department, College of Science, King Saud University, PO Box 2455, Riyadh 11451, Saudi Arabia (email: ialolyan05@yahoo.com)
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Abstract

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Computing a zero of a continuous function is an old and extensively researched problem in numerical computation. In this paper, we present an efficient subdivision algorithm for finding all real roots of a function in multiple variables. This algorithm is based on a simple computationally verifiable necessity test for the existence of a root in any compact set. Both theoretical analysis and numerical simulations demonstrate that the algorithm is very efficient and reliable. Convergence is shown and numerical examples are presented.

Keywords

numerical solution of nonlinear system of equationexclusion testdecomposable functionscomputational complexity

MSC classification

Secondary: 65H10: Systems of equations 65Y20: Complexity and performance of numerical algorithms
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 3 , June 2008 , pp. 353 - 363
Copyright
Copyright © 2008 Australian Mathematical Society

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