No Access

CONSTRUCTION OF DERIVATIVE-FREE ITERATIVE METHODS FROM CHEBYSHEV'S METHOD

J. A. EZQUERRO

Department of Mathematics and Computation, University of La Rioja, 26004 Logroño, Spain

Search for more papers by this author

A. GRAU

Department of Applied Mathematics II, Technical University of Catalonia, 08034 Barcelona, Spain

Search for more papers by this author

M. GRAU-SÁNCHEZ

Department of Applied Mathematics II, Technical University of Catalonia, 08034 Barcelona, Spain

Search for more papers by this author

, and

M. A. HERNÁNDEZ

Department of Mathematics and Computation, University of La Rioja, 26004 Logroño, Spain

Search for more papers by this author

https://doi.org/10.1142/S0219530513500097Cited by:8 (Source: Crossref)

Abstract

From some modifications of Chebyshev's method, we consider a uniparametric family of iterative methods that are more efficient than Newton's method, and we then construct two iterative methods in a similar way to the Secant method from Newton's method. These iterative methods do not use derivatives in their algorithms and one of them is more efficient than the Secant method, which is the classical method with this feature.

Keywords:

AMSC: 47H17, 65J15

References

I. K. Argyros, Mh. Math. 106, 85 (1988), DOI: 10.1007/BF01298829. Crossref, Web of Science, Google Scholar
I. K. Argyros, Publ. Math. Debrecen 43(4), 223 (1993). Crossref, Web of Science, Google Scholar
J. A. Ezquerro and M. A. Hernández, J. Complexity 25, 343 (2009), DOI: 10.1016/j.jco.2009.04.001. Crossref, Web of Science, Google Scholar
J. A. Ezquerroet al., J. Optim. Theory Appl. 151(1), 163 (2011), DOI: 10.1007/s10957-011-9870-y. Crossref, Web of Science, Google Scholar
M. Grau-Sánchez, M. Noguera and J. M. Gutiérrez, Appl. Math. Lett. 23, 472 (2010). Crossref, Web of Science, Google Scholar
L. V. Kantorovich and G. P. Akilov , Functional Analysis ( Pergamon Press , Oxford , 1982 ) . Google Scholar
A. M. Ostrowski , Solutions of Equations in Euclidean and Banach Spaces ( Academic Press , New York , 1973 ) . Google Scholar
A. D. Polyanin and A. V. Manzhirov , Handbook of Integral Equations ( CRC Press , Boca Ratón , 1998 ) . Crossref, Google Scholar
F. A. Potra and V. Pták , Nondiscrete Induction and Iterative Methods ( Pitman Publishing Limited , London , 1984 ) . Google Scholar
S. M. Shakhno, J. Comput. Appl. Math. 231, 222 (2009), DOI: 10.1016/j.cam.2009.02.010. Crossref, Web of Science, Google Scholar
J. F. Traub , Iterative Methods for the Solution of Equations ( Prentice-Hall , Englewood Cliffs, New Jersey , 1964 ) . Google Scholar