TY - JOUR
T1 - An Algorithm that Localizes and Counts the Zeros of a $C^2$-Function
AU - Hungerbühler , Norbert
AU - Wu , Rui
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 320
EP - 333
PY - 2020
DA - 2020/03
SN - 13
DO - http://doi.org/10.4208/nmtma.OA-2019-0077
UR - https://global-sci.org/intro/article_detail/nmtma/15450.html
KW - Number of zeros on an interval.
AB - <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>