Year: 2020
Author: Rui Wu, Norbert Hungerbühler, Rui Wu
Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 2 : pp. 320–333
Abstract
We describe an algorithm that localizes the zeros of a given real $C^2$-function $f$ on an interval $[a,b]$. The algorithm generates a sequence of subintervals which contain a single zero of $f$. In particular, the exact number of zeros of $f$ on $[a,b]$ can be determined in this way. Apart from $f$, the only additional input of the algorithm is an upper and a lower bound for $f''$. We also show how the intervals determined by the algorithm can be further refined until they are contained in the basin of attraction of the Newton method for the corresponding zero.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2019-0077
Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 2 : pp. 320–333
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Number of zeros on an interval.