An integral that counts the zeros of a function
- Hungerbühler, Norbert Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092, Zürich, Switzerland
- Wasem, Micha HTA Freiburg, HES-SO University of Applied Sciences and Arts Western Switzerland, Pérolles 80, 1700, Freiburg, Switzerland
Published in:
- Open Mathematics. - Walter de Gruyter GmbH. - 2018, vol. 16, no. 1, p. 1621-1633
English
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.
- Language
-
- English
- Open access status
- gold
- Identifiers
-
- DOI 10.1515/math-2018-0131
- ISSN 2391-5455
- Persistent URL
- https://sonar.ch/global/documents/114192
Export to…
Statistics
Document views: 62
File downloads:
- Full-text: 0