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Enclosing all zeros of an analytic function: a rigorous approach
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2009 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 228, no 1, 418-423 p.Article in journal (Refereed) Published
Abstract [en]

We present a method to find all zeros of an analytic function in a rectangular domain. The approach is based on finding guaranteed enclosures rather than approximations of the zeros. Well-isolated simple zeros are determined fast and with high accuracy. Clusters of zeros can in many cases be distinguished from multiple zeros by applying the argument principle to sufficiently high-order derivatives of the function. We illustrate the proposed method through five examples of varying levels of complexity.

Place, publisher, year, edition, pages
2009. Vol. 228, no 1, 418-423 p.
Keyword [en]
Rigorous numerics, Argument principle, Root finding, Interval analysis
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-103151DOI: 10.1016/j.cam.2008.10.014ISI: 000265892700043OAI: oai:DiVA.org:uu-103151DiVA: diva2:217592
Available from: 2009-05-14 Created: 2009-05-14 Last updated: 2017-12-13Bibliographically approved
In thesis
1. On some computer-aided proofs in analysis
Open this publication in new window or tab >>On some computer-aided proofs in analysis
2007 (English)Licentiate thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, Uppsala University, 2007. 14 p.
Series
U.U.D.M. report / Uppsala University, Department of Mathematics, ISSN 1101-3591 ; 2007:29
National Category
Mathematics
Research subject
Mathematics; Mathematics
Identifiers
urn:nbn:se:uu:diva-141509 (URN)
Opponent
Supervisors
Available from: 2011-01-12 Created: 2011-01-12 Last updated: 2011-01-12Bibliographically approved

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Johnson, Tomas

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