×

A family of multi-point iterative methods for solving systems of nonlinear equations. (English) Zbl 1154.65037

This paper extends a known multi-point family of iterative methods for solving nonlinear equations to the \(n\)-dimensional case. A local convergence analysis and numerical examples are provided.

MSC:

65H10 Numerical computation of solutions to systems of equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Werner, W., Some improvements of classical iterative methods for the solution of nonlinear equations, (Allgower, El.; Glashoff, K.; Peitgen., H. O., Numerical Solution of Nonlinear Equations (Proc., Bremen, 1980). Numerical Solution of Nonlinear Equations (Proc., Bremen, 1980), Lecture Notes in Math., vol. 879 (1981)), 427-440 · Zbl 0494.65033
[2] Argyros, I. K.; Szidarovszky, F., The Theory and Applications of Iterations Methods (1993), CRC Press: CRC Press Boca Raton, FL · Zbl 0844.65052
[3] Gutiérrez, J. M.; Hernández, M. A., A family of Chebyshev-Halley type methods in Banach spaces, Bull. Austral. Math. Soc., 55, 113-130 (1997) · Zbl 0893.47043
[4] Amat, S.; Busquier, S.; Gutiérrez, J. M., Geometric constructions of iterative functions to solve nonlinear equations, J. Comput. Appl. Math., 157, 197-205 (2003) · Zbl 1024.65040
[5] Frontini, M.; Sormani, E., Some variant of Newton’s method with third-order convergence, Appl. Math. Comput., 140, 2-3, 419-426 (2003) · Zbl 1037.65051
[6] Argyros, I. K.; Chen, D.; Qian, Q., Optimal-order parameter identification in solving nonlinear systems in a Banach space, J. Comput. Math., 13, 267-280 (1995) · Zbl 0831.65060
[7] Han, D., The convergence on a family of iterations with cubic order, J. Comput. Math., 19, 5, 467-474 (2001) · Zbl 1008.65035
[8] Nedzhibov, G. H.; Hasanov, V. I.; Petkov, M. P., On some families of multi-point iterative methods for solving nonlinear equations, Numer. Algor., 42, 127-136 (2006) · Zbl 1117.65067
[9] Traub, J. F., Iterative Methods for the Solution of Equations (1964), Prentice Hall: Prentice Hall Englewood Cliffs, New Jersey · Zbl 0121.11204
[10] Jarrat, P., Some fourth order multipoint iterative methods for solving equations, Math. Comp., 20, 434-437 (1966) · Zbl 0229.65049
[11] Argyros, I. K.; Chen, D.; Qian, Q., The Jarratt method in Banach space setting, J. Comput. Appl. Math., 51, 103-106 (1994) · Zbl 0809.65054
[12] Ezquerro, J. A.; Gutiérrez, J. M.; Hernández, M. A.; Salanova, M. A., A biparametric family of inverse-free multipoint iterations, Comput. Appl. Math., 19, 1, 109-124 (2000) · Zbl 1344.65051
[13] Ortega, J. M.; Rheinboldt, W. S., Iterative Solution of Nonlinear Equations in Several Variables (1970), Academic Press: Academic Press New York · Zbl 0241.65046
[14] Weerakoon, S.; Fernando, T. G.I., A variant of Newton’s method with accelerated third-order convergence, Appl. Math. Lett., 13, 87-93 (2000) · Zbl 0973.65037
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.