Enclosing all zeros of an analytic function: a rigorous approach
2009 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, Vol. 228, no 1, 418-423 p.Article in journal (Refereed) Published
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.
Rigorous numerics, Argument principle, Root finding, Interval analysis
Research subject Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-103151DOI: 10.1016/j.cam.2008.10.014ISI: 000265892700043OAI: oai:DiVA.org:uu-103151DiVA: diva2:217592