Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
special section
Verified computation of a disc containing exactly k roots of a univariate nonlinear function
Siegfried M. RumpShin'ichi Oishi
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2010 Volume 1 Issue 1 Pages 89-96

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Abstract

It is well known that it is an ill-posed problem to decide whether a function has a multiple root. For example, an arbitrarily small perturbation of a real polynomial may change a double real root into two distinct real or complex roots. In this paper we describe a computational method for the verified computation of a complex disc to contain exactly k roots of a univariate nonlinear function. The function may be given by some program. Computational results using INTLAB, the Matlab toolbox for reliable computing, demonstrate properties and limits of the method.

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© 2010 The Institute of Electronics, Information and Communication Engineers
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