Vol. 9, No. 2, 2014

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ISSN: 2157-5452 (e-only)
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A new class of secant-like methods for solving nonlinear systems of equations

José A. Ezquerro, Angela Grau, Miquel Grau-Sánchez and Miguel A. Hernández-Verón

Vol. 9 (2014), No. 2, 201–213
Abstract

Applying twice an idea of Hernández and Rubio (2002) for constructing a one-parameter family of secant-like methods, we define a two-parameter family of secant-like methods for solving nonlinear systems of equations. We analyze the efficiency of this new family and conclude that the Kurchatov method, which is one member of the family, is the most efficient. We illustrate this with Troesch’s problem.

Keywords
nonlinear equations, iterative methods, divided difference, secant method, Kurchatov method, secant-like method, order of convergence, efficiency index, computational efficiency
Mathematical Subject Classification 2010
Primary: 47H99, 65H10
Milestones
Received: 29 March 2012
Revised: 15 October 2012
Accepted: 20 February 2013
Published: 26 July 2014
Authors
José A. Ezquerro
Department of Mathematics and Computation
University of La Rioja
26004 Logroño
Spain
Angela Grau
Department of Applied Mathematics II
Technical University of Catalonia
08034 Barcelona
Spain
Miquel Grau-Sánchez
Department of Applied Mathematics II
Technical University of Catalonia
08034 Barcelona
Spain
Miguel A. Hernández-Verón
Department of Mathematics and Computation
University of La Rioja
26004 Logroño
Spain