On the geometry of Householder’s and Halley’s methods

Reference : On the geometry of Householder’s and Halley’s methods


	Document type :	Dissertations and theses : Other
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/47708

Title :	On the geometry of Householder’s and Halley’s methods
Language :	English
Author, co-author :	Palmirotta, Guendalina [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
Publication date :	Dec-2015
Institution :	University of Luxembourg, Luxembourg
Name of the degree :	Project
Supervisor :	Marichal, Jean-Luc
Abstract :	[en] In this paper, some modified Newton’s methods for solving nonlinear equations are proposed. Householder and Halley have suggested a variant of New- ton’s method in which they take an osculating parabola respectively an hyperbola instead of the tangent line. The proposed methods go faster to approximated solution, but it requires more calculation efforts. The order of convergence of both methods is three. By some interesting numerical problems, the theoretical results are illustrated. In the appendix, we give a foretaste of the proposed methods in the complex plane.
Permalink :	http://hdl.handle.net/10993/47708

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