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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.
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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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