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Enclosing all zeros of a system of analytic functions
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Max Planck Inst Quantum Opt, Hans Kopfermann Str 1, D-85748 Garching, Germany;ASCR, Inst Phys, ELI Beamlines Project, Na Slovance 2, Prague 18221, Czech Republic.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2019 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 348, p. 513-522Article in journal (Refereed) Published
Abstract [en]

We present a rigorous numerical method for location of simple zeros of a system of two analytic functions in a rectangular cuboid domain based on the logarithmic integral. We compare this to a simpler, also rigorous, method based on bisection. The latter is determined to be more efficient in the examples considered. This is mainly due to inefficient methods for computing the logarithmic integral occurring in the former method. (C) 2018 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
Elsevier, 2019. Vol. 348, p. 513-522
Keywords [en]
Rigorous numerics, Argument principle, Root finding, Interval analysis, Systems of analytic functions
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:uu:diva-376707DOI: 10.1016/j.amc.2018.08.041ISI: 000456796600034OAI: oai:DiVA.org:uu-376707DiVA, id: diva2:1288573
Funder
Swedish Research Council, 2013-4964Available from: 2019-02-13 Created: 2019-02-13 Last updated: 2019-02-13Bibliographically approved

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Dahne, JoelTucker, Warwick

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