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Title: A global analysis of Newton iterations for determining turning points (English)
Author: Janovský, Vladimír
Author: Seige, Viktor
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 38
Issue: 4
Year: 1993
Pages: 323-360
Summary lang: English
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Category: math
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Summary: The global convergence of a direct method for determining turning (limit) points of a parameter-dependent mapping is analysed. It is assumed that the relevant extended system has a singular root for a special parameter value. The singular root is clasified as a $bifurcation singularity$ (i.e., as a $degenerate$ turning point). Then, the Theorz for Imperfect Bifurcation offers a particular scenario for the split of the singular root into a finite number of regular roots (turning points) due to a given parameter imperfection. The relationship between the scenario and the actual performance of Newton method is studied. Both theoretical and experimental arguments are presented in order to quaetion the claim that a particular bifurcation singularity $organiyes$ the Newton method assuming small parameter perturbations. (English)
Keyword: detection of turning points
Keyword: Newton method
Keyword: Newton flow
Keyword: basins of attraction
Keyword: qualitative analysis
Keyword: normal forms of the flow
Keyword: global convergence
Keyword: singularity theory
Keyword: bifurcation singularity
Keyword: imperfect bifurcation
MSC: 37G99
MSC: 58C15
MSC: 65H17
MSC: 65H20
idZBL: Zbl 0806.65052
idMR: MR1228512
DOI: 10.21136/AM.1993.104559
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Date available: 2008-05-20T18:46:08Z
Last updated: 2020-07-28
Stable URL: http://hdl.handle.net/10338.dmlcz/104559
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