Cordero Barbero, A.; Torregrosa Sánchez, JR. (2011). A class of Steffensen type methods with optimal order of convergente. Applied Mathematics and Computation. 217(19):7653-7659. https://doi.org/10.1016/j.amc.2011.02.067
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/52542
Title:
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A class of Steffensen type methods with optimal order of convergente
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Author:
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Cordero Barbero, Alicia
Torregrosa Sánchez, Juan Ramón
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UPV Unit:
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Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
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Issued date:
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Abstract:
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In this paper, a family of Steffensen type methods of fourth-order convergence for solving nonlinear smooth equations is suggested. In the proposed methods, a linear combination of divided differences is used to get a ...[+]
In this paper, a family of Steffensen type methods of fourth-order convergence for solving nonlinear smooth equations is suggested. In the proposed methods, a linear combination of divided differences is used to get a better approximation to the derivative of the given function. Each derivative-free member of the family requires only three evaluations of the given function per iteration. Therefore, this class of methods has efficiency index equal to 1.587. Kung and Traub conjectured that the order of convergence of any multipoint method without memory cannot exceed the bound 2d-1, where d is the number of functional evaluations per step. The new class of methods agrees with this conjecture for the case d=3. Numerical examples are made to show the performance of the presented methods, on smooth and nonsmooth equations, and to compare with other ones. © 2011 Elsevier Inc. All rights reserved.
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Subjects:
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Convergence order
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Derivative free method
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Efficiency index
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Iterative methods
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Nonlinear equations
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Steffensen's method
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Class of methods
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Derivative-free
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Divided difference
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Fourth-order
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Functional evaluation
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Linear combinations
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Multi-point methods
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Nonsmooth equation
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Numerical example
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Optimal order of convergence
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Order of convergence
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Type methods
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Function evaluation
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Numerical methods
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Copyrigths:
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Reserva de todos los derechos
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Source:
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Applied Mathematics and Computation. (issn:
0096-3003
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DOI:
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10.1016/j.amc.2011.02.067
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Publisher:
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Elsevier
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Publisher version:
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http://dx.doi.org/10.1016/j.amc.2011.02.067
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Project ID:
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info:eu-repo/grantAgreement/MICINN//MTM2010-18539/ES/DISEÑO, ANALISIS Y OPTIMIZACION DE METODOS DE RESOLUCION DE ECUACIONES Y SISTEMAS NO LINEALES. APLICACIONES A PROBLEMAS DE VALOR INICIAL Y FLUJO OPTICO/
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Thanks:
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This research was supported by Ministerio de Ciencia y Tecnologia MTM2010-18539.
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Type:
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Artículo
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