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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 |
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Vol. 9 (2014), No. 2, 201–213
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 47H99, 65H10
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Milestones
Received: 29 March 2012
Revised: 15 October 2012
Accepted: 20 February 2013
Published: 26 July 2014
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Authors |
| José A. Ezquerro | |
| Department of Mathematics and
Computation University of La Rioja 26004 Logroño Spain |
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| Angela Grau | |
| Department of Applied Mathematics
II Technical University of Catalonia 08034 Barcelona Spain |
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| Miquel Grau-Sánchez | |
| Department of Applied Mathematics
II Technical University of Catalonia 08034 Barcelona Spain |
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| Miguel A. Hernández-Verón | |
| Department of Mathematics and
Computation University of La Rioja 26004 Logroño Spain |
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