An integral that counts the zeros of a function
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Date
2018
Publication Type
Journal Article
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yes
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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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published
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Journal / series
Volume
16
Pages / Article No.
1 - 14
Publisher
De Gruyter
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Software
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Subject
number of zeros on an interval; multiplicity of zeros
Organisational unit
03874 - Hungerbühler, Norbert / Hungerbühler, Norbert