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New family of iterative methods with high order of convergence for solving nonlinear systems

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New family of iterative methods with high order of convergence for solving nonlinear systems

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Cordero Barbero, A.; Torregrosa Sánchez, JR.; Penkova Vassileva, M. (2013). New family of iterative methods with high order of convergence for solving nonlinear systems. En Numerical Analysis and Its Applications. Springer Verlag. 222-230. https://doi.org/10.1007/978-3-642-41515-9_23

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/56036

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Title: New family of iterative methods with high order of convergence for solving nonlinear systems
Author: Cordero Barbero, Alicia Torregrosa Sánchez, Juan Ramón Penkova Vassileva, María
UPV Unit: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Issued date:
Abstract:
In this paper we present and analyze a set of predictor-corrector iterative methods with increasing order of convergence, for solving systems of nonlinear equations. Our aim is to achieve high order of convergence with few ...[+]
Subjects: Nonlinear systems , Iterative methods , Jacobian matrix , Convergence order , Efficiency index
Copyrigths: Reserva de todos los derechos
ISBN: 978-3-642-41514-2
Source:
Numerical Analysis and Its Applications. (issn: 0302-9743 ) (eissn: 1611-3349 )
DOI: 10.1007/978-3-642-41515-9_23
Publisher:
Springer Verlag
Publisher version: http://dx.doi.org/10.1007/978-3-642-41515-9_23
Series: Lecture Notes in Computer Science;8236
Project ID:
info:eu-repo/grantAgreement/MICINN//MTM2011-28636-C02-02/ES/DISEÑO Y ANALISIS DE METODOS EFICIENTES DE RESOLUCION DE ECUACIONES Y SISTEMAS NO LINEALES/
info:eu-repo/grantAgreement/FONDOCYT//2011-1-B1-33/
Thanks:
This research was supported by Ministerio de Ciencia y Tecnología MTM2011-28636-C02-02 and by FONDOCYT 2011-1-B1-33, República Dominicana.
Type: Capítulo de libro

References

Cordero, A., Hueso, J.L., Martínez, E., Torregrosa, J.R.: A modified Newton-Jarratt’s composition. Numer. Algor. 55, 87–99 (2010)

Cordero, A., Hueso, J.L., Martínez, E., Torregrosa, J.R.: Efficient high-order methods based on golden ratio for nonlinear systems. Applied Mathematics and Computation 217(9), 4548–4556 (2011)

Cordero, A., Torregrosa, J.R.: Variants of Newton’s Method using fifth-order quadrature formulas. Applied Mathematics and Computation 190, 686–698 (2007) [+]
Cordero, A., Hueso, J.L., Martínez, E., Torregrosa, J.R.: A modified Newton-Jarratt’s composition. Numer. Algor. 55, 87–99 (2010)

Cordero, A., Hueso, J.L., Martínez, E., Torregrosa, J.R.: Efficient high-order methods based on golden ratio for nonlinear systems. Applied Mathematics and Computation 217(9), 4548–4556 (2011)

Cordero, A., Torregrosa, J.R.: Variants of Newton’s Method using fifth-order quadrature formulas. Applied Mathematics and Computation 190, 686–698 (2007)

Cordero, A., Torregrosa, J.R.: On interpolation variants of Newton’s method for functions of several variables. Journal of Computational and Applied Mathematics 234, 34–43 (2010)

Cordero, A., Torregrosa, J.R., Vassileva, M.P.: Pseudocomposition: a technique to design predictor-corrector methods for systms of nonlinear equtaions. Applied Mathematics and Computation 218(23), 11496–11504 (2012)

Nikkhah-Bahrami, M., Oftadeh, R.: An effective iterative method for computing real and complex roots of systems of nonlinear equations. Applied Mathematics and Computation 215, 1813–1820 (2009)

Ostrowski, A.M.: Solutions of equations and systems of equations. Academic Press, New York (1966)

Shin, B.-C., Darvishi, M.T., Kim, C.-H.: A comparison of the Newton-Krylov method with high order Newton-like methods to solve nonlinear systems. Applied Mathematics and Computation 217, 3190–3198 (2010)

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