Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 320-333.
Published online: 2020-03
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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.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2019-0077}, url = {http://global-sci.org/intro/article_detail/nmtma/15450.html} }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.