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New predictor-corrector methods with high efficiency for solving nonlinear systems

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New predictor-corrector methods with high efficiency for solving nonlinear systems

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Cordero Barbero, A.; Torregrosa Sánchez, JR.; Penkova Vassileva, M. (2012). New predictor-corrector methods with high efficiency for solving nonlinear systems. Journal of Applied Mathematics. 2012. https://doi.org/10.1155/2012/709843

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Título: New predictor-corrector methods with high efficiency for solving nonlinear systems
Autor: Cordero Barbero, Alicia Torregrosa Sánchez, Juan Ramón Penkova Vassileva, María
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
A new set of predictor-corrector iterative methods with increasing order of convergence is proposed in order to estimate the solution of nonlinear systems. Our aim is to achieve high order of convergence with few Jacobian ...[+]
Palabras clave: Newton's method , Variants
Derechos de uso: Reconocimiento (by)
Fuente:
Journal of Applied Mathematics. (issn: 1110-757X ) (eissn: 1687-0042 )
DOI: 10.1155/2012/709843
Editorial:
Hindawi Publishing Corporation
Versión del editor: http://dx.doi.org/10.1155/2012/709843
Código del Proyecto:
info:eu-repo/grantAgreement/MICINN//MTM2011-28636-C02-02/ES/DISEÑO Y ANALISIS DE METODOS EFICIENTES DE RESOLUCION DE ECUACIONES Y SISTEMAS NO LINEALES/
Agradecimientos:
The authors would like to thank the referees for the valuable comments and for the suggestions to improve the readability of the paper. This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02 ...[+]
Tipo: Artículo

References

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He, Y., & Ding, C. H. Q. (2001). The Journal of Supercomputing, 18(3), 259-277. doi:10.1023/a:1008153532043

Revol, N., & Rouillier, F. (2005). Motivations for an Arbitrary Precision Interval Arithmetic and the MPFI Library. Reliable Computing, 11(4), 275-290. doi:10.1007/s11155-005-6891-y [+]
Bruns, D. D., & Bailey, J. E. (1977). Nonlinear feedback control for operating a nonisothermal CSTR near an unstable steady state. Chemical Engineering Science, 32(3), 257-264. doi:10.1016/0009-2509(77)80203-0

He, Y., & Ding, C. H. Q. (2001). The Journal of Supercomputing, 18(3), 259-277. doi:10.1023/a:1008153532043

Revol, N., & Rouillier, F. (2005). Motivations for an Arbitrary Precision Interval Arithmetic and the MPFI Library. Reliable Computing, 11(4), 275-290. doi:10.1007/s11155-005-6891-y

Cordero, A., Hueso, J. L., Martínez, E., & Torregrosa, J. R. (2009). A modified Newton-Jarratt’s composition. Numerical Algorithms, 55(1), 87-99. doi:10.1007/s11075-009-9359-z

Nikkhah-Bahrami, M., & Oftadeh, R. (2009). An effective iterative method for computing real and complex roots of systems of nonlinear equations. Applied Mathematics and Computation, 215(5), 1813-1820. doi:10.1016/j.amc.2009.07.028

Shin, B.-C., Darvishi, M. T., & Kim, C.-H. (2010). A comparison of the Newton–Krylov method with high order Newton-like methods to solve nonlinear systems. Applied Mathematics and Computation, 217(7), 3190-3198. doi:10.1016/j.amc.2010.08.051

Cordero, A., Hueso, J. L., Martínez, E., & Torregrosa, J. R. (2011). Efficient high-order methods based on golden ratio for nonlinear systems. Applied Mathematics and Computation, 217(9), 4548-4556. doi:10.1016/j.amc.2010.11.006

Dayton, B. H., Li, T.-Y., & Zeng, Z. (2011). Multiple zeros of nonlinear systems. Mathematics of Computation, 80(276), 2143-2143. doi:10.1090/s0025-5718-2011-02462-2

Cordero, A., Torregrosa, J. R., & Vassileva, M. P. (2012). Pseudocomposition: A technique to design predictor–corrector methods for systems of nonlinear equations. Applied Mathematics and Computation, 218(23), 11496-11504. doi:10.1016/j.amc.2012.04.081

Cordero, A., & Torregrosa, J. R. (2010). On interpolation variants of Newton’s method for functions of several variables. Journal of Computational and Applied Mathematics, 234(1), 34-43. doi:10.1016/j.cam.2009.12.002

Cordero, A., & Torregrosa, J. R. (2007). Variants of Newton’s Method using fifth-order quadrature formulas. Applied Mathematics and Computation, 190(1), 686-698. doi:10.1016/j.amc.2007.01.062

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