Newton's methods from a geometric point of view.
F. Presas (2001)
Extracta Mathematicae
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F. Presas (2001)
Extracta Mathematicae
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Gwoździewicz, Janusz (2008)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Uko, Livinus U., Velásquez Ossa, Raúl Eduardo (2001)
Revista Colombiana de Matemáticas
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Alexander Esterov (2005)
Revista Matemática Complutense
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A formula of Matsuo Oka (1990) expresses the Milnor number of a germ of a complex analytic map with a generic principal part in terms of the Newton polyhedra of the components of the map. In this paper this formula is generalized to the case of the index of a 1-form on a local complete intersection singularity (Theorem 1.10, Corollaries 1.11, 4.1). In particular, the Newton polyhedron of a 1-form is defined (Definition 1.6). This also simplifies the Oka formula in some particular cases...
Rajković, Predrag M., Stanković, Miomir S., Marinković, Slađana D. (2003)
Novi Sad Journal of Mathematics
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Argyros, Ioannis K. (2006)
Revista Colombiana de Matemáticas
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Rubeša, Jelena, Kunisch, Karl (2010)
Mathematica Balkanica New Series
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AMS Subj. Classification: 49J15, 49M15 The control problem of minimal time transition between two stationary points are formulated in a framework of an indirect numerical method. The problem is regularized and the monotone behavior of the regularisation procedure is investigated. Semi-smooth Newton method applied on the regularized problems converge superlinearly and usually produce a very accurate solution. Differently from other methods, this one does not need a-priory knowledge...
Aaron Melman (2011)
Matematički Vesnik
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Karatson, Janos, Neuberger, John W. (2007)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Argyros, Ioannis K. (2006)
Revista Colombiana de Matemáticas
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A. Melman (2010)
Matematički Vesnik
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Argyros, Ioannis K., Hilout, Said (2009)
The Journal of Nonlinear Sciences and its Applications
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