Method for Localizing the Zeros of Analytic Functions Based on the Krawczyk Operator

The problem of localizing the zeros of analytic functions using the Krawczyk operator is considered. Formulas are obtained for computing the image of the Krawczyk operator for analytic functions. Based on this, a new algorithm for localizing the zeros is proposed. The use of the method is demonstrat...

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Bibliographic Details
Published in:Cybernetics and systems analysis 2019-05, Vol.55 (3), p.514-520
Main Authors: Semenov, V. Yu, Semenova, E. V.
Format: Article
Language:English
Subjects:
Algorithms
Analytic functions
Artificial Intelligence
Control
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators (mathematics)
Processor Architectures
Software Engineering/Programming and Operating Systems
Systems Theory
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Summary:The problem of localizing the zeros of analytic functions using the Krawczyk operator is considered. Formulas are obtained for computing the image of the Krawczyk operator for analytic functions. Based on this, a new algorithm for localizing the zeros is proposed. The use of the method is demonstrated by numerical examples including the search for the zeros of the Riemann zeta function.
ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-019-00159-y