@Article{NMTMA-13-320,
author = {Hungerbühler , Norbert and Wu , Rui},
title = {An Algorithm that Localizes and Counts the Zeros of a $C^2$-Function},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2020},
volume = {13},
number = {2},
pages = {320--333},
abstract = {<p style="text-align: justify;">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 $f&#39;&#39;$. 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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2019-0077},
url = {http://global-sci.org/intro/article_detail/nmtma/15450.html}
}