Seventh-order derivative-free iterative method for solving nonlinear systems (original) (raw)
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References
- Ortega, J.M., Rheinbolt, W.C.: Iterative Solution of Nonlinear Equations in SeveralVariables. Academic Press, New York (1970)
Google Scholar - Traub, J.F.: Iterative Methods for the Solution of Equations. Prentice-Hall, New Jersey (1964)
MATH Google Scholar - Dembo, R.S., Eisenstat, S.C., Steihaug, T.: Inexact Newton methods. SIAM. J. Numer. Anal 19, 400–408 (1982)
Article MATH MathSciNet Google Scholar - Broyden, C.G.: A class of methods for solving nonlinear simultaneous equations. Math. Comput 19, 577–593 (1965)
Article MATH MathSciNet Google Scholar - Liu, Z., Zheng, Q., Zhao, P.: A variant of Steffensen’s method of fourth-order convergence and its applications. Appl. Math. Comput 216, 1978–1983 (2010)
Article MATH MathSciNet Google Scholar - Sharma, J.R., Arora, H.: An efficient derivative free iterative method for solving systems of nonlinear equations. Appl. Anal. Discrete Math 7, 390–403 (2013)
Article MATH MathSciNet Google Scholar - Wang, X., Zhang, T.: A family of steffensen type methods with seventh-order convergence. Numer. Algor 2, 429–444 (2013)
Article Google Scholar - Grau-Sánchez, M., Noguera, M., Amat, S.: On the approximation of derivatives using divided difference operators preserving the local convergence order of iterative methods. J. Comput. Appl. Math 237, 263–272 (2013)
Article Google Scholar - Grau-Sánchez, M., Grau, À., Noguera, M.: Frozen divided difference scheme for solving systems of nonlinear equations. J. Comput. Appl. Math 235, 1739–1743 (2011)
Article MATH MathSciNet Google Scholar - Ezquerro, J.A., Hernández, M.A., Romero, N.: Solving nonlinear integral equations of Fredholm type with high order iterative methods. J. Comput. Appl. Math 36, 1449–1463 (2011)
Article Google Scholar - Ezquerro, J.A., Grau, À., Grau-Sánchez, M., Hernández, M.A., Noguera, M.: Analysing the efficiency of some modifications of the secant method. Comput. Math. Appl 64, 2066–2073 (2012)
Article MATH MathSciNet Google Scholar - Grau-Sánchez, M., Noguera, M.: A technique to choose the most efficient method between secant method and some variants. Appl. Math. Comput 218, 6415–6426 (2012)
Article MATH MathSciNet Google Scholar - Fousse, L., Hanrot, G., Lefèvre, V., Pélissier, P., Zimmermann, P.: MPFR: a multiple-precision binary floating-point library with correct rounding. ACM Trans. Math. Softw 33, 15–16 (2007)
Article Google Scholar - http://www.mpfr.org/mpfr.org/mpfr-2.1.0/timings.html
- Grau-Sánchez, M., Noguera, M., Gutiérrez, J.M.: On some computational orders of convergence. Appl. Math. Lett 23, 472–478 (2010)
Article MATH MathSciNet Google Scholar - Amat, S., Busquier, S., Grau, À., Grau-Sánchez, M.: Maximum efficiency for a family of Newton-like methods with frozen derivatives and some applications. Appl. Math. Comput. 219, 7954–7963 (2013)
Article MATH MathSciNet Google Scholar - Sharma, J.R., Arora, H.: On efficient weighted-Newton methods for solving systems of nonlinear equations. Appl. Math. Comput. 222, 497–506 (2013)
Article MathSciNet Google Scholar - Potra, F.-A., Pták, V.: Nondiscrete Induction and Iterative Processes. Pitman Publishing, Boston (1984)
MATH Google Scholar