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arXiv · 1808.09690

An integral that counts the zeros of a function

Norbert Hungerbühler·Micha Wasem
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Abstract

Given a real function $f$ on an interval $[a,b]$ satisfying mild regularity conditions, we determine the number of zeros of $f$ by evaluating a certain integral. The integrand depends on $f, f'$ and $f''$. In particular, by approximating the integral with the trapezoidal rule on a fine enough grid, we can compute the number of zeros of $f$ by evaluating finitely many values of $f,f'$ and $f''$. A variant of the integral even allows to determine the number of the zeros broken down by their multiplicity.

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Norbert Hungerbühler, Micha Wasem. 2018-08-29. An integral that counts the zeros of a function. https://doi.org/10.1515/math-2018-0131

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