An integral that counts the zeros of a function

Wednesday, 29 August, 2018

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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.


Norbert Hungerbühler
Micha Wasem