Reference : On the geometry of Householder’s and Halley’s methods
Dissertations and theses : Other
Physical, chemical, mathematical & earth Sciences : Mathematics
On the geometry of Householder’s and Halley’s methods
Palmirotta, Guendalina mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
University of Luxembourg, ​​Luxembourg
Marichal, Jean-Luc mailto
[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.

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