Expanding the Applicability of High-Order Traub-Type Iterative Procedures

We propose a collection of hybrid methods combining Newton’s method with frozen derivatives and a family of high-order iterative schemes. We present semilocal convergence results for this collection on a Banach space setting. Using a more precise majorizing sequence and under the same or weaker convergence conditions than the ones in earlier studies, we expand the applicability of these iterative procedures.

[1]  James M. Ortega,et al.  Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[2]  Petko D. Proinov.  New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems , 2010, J. Complex..

[3]  F. Potra,et al.  The rate of convergence of a modified Newton's process , 1981 .

[4]  I. Argyros,et al.  Computational Methods in Nonlinear Analysis:Efficient Algorithms, Fixed Point Theory and Applications , 2013 .

[5]  F. Potra,et al.  Nondiscrete induction and iterative processes , 1984 .

[6]  M. J. Legaz,et al.  On a Family of High-Order Iterative Methods under Kantorovich Conditions and Some Applications , 2012 .

[7]  L. B. Rall,et al.  Computational Solution of Nonlinear Operator Equations , 1969 .

[8]  Miguel Ángel Hernández,et al.  An improvement of the region of accessibility of Chebyshev's method from Newton's method , 2009, Math. Comput..

[9]  Y. Cho,et al.  Numerical Methods for Equations and its Applications , 2012 .

[10]  Peter Deuflhard,et al.  Newton Methods for Nonlinear Problems , 2004 .

[11]  Ioannis K. Argyros,et al.  Weaker conditions for the convergence of Newton's method , 2012, J. Complex..

[12]  P. Deuflhard.  Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms , 2011 .

[13]  F. Potra,et al.  A generalization of regula falsi , 1980 .

[14]  J. Traub.  Iterative Methods for the Solution of Equations , 1982 .

[15]  F. Potra,et al.  On a class of modified newton processes , 1980 .

[16]  W. Rheinboldt.  A unified convergence theory for a class of iterative processes. , 1968 .