Results 11 to 20 of about 677,232 (187)

On the semilocal convergence of efficient Chebyshev–Secant-type methods [PDF]

Journal of Computational and Applied Mathematics, 2011
We introduce a three-step Chebyshev–Secant-type method (CSTM) with high efficiency index for solving nonlinear equations in a Banach space setting. We provide a semilocal convergence analysis for (CSTM) using recurrence relations.
Argyros, null, J.A. Ezquerro, M.A. Hernández, J.M. Gutiérrez, I.K. Argyros, S. Hilout, Hilout, null, Gutiérrez, null [0000-0002-0434-7250], Hernández, null [0000-0001-5478-2958], Ezquerro, null [0000-0001-8120-167X], Hernández, null, Gutiérrez, null, Ezquerro, null   +12 more
core   +6 more sources

Semilocal convergence of the secant method under mild convergence conditions of differentiability [PDF]

Computers & Mathematics with Applications, 2002
In this work, we obtain a semilocal convergence result for the secant method in Banach spaces under mild convergence conditions. We consider a condition for divided differences which generalizes those usual ones, i.e., Lipschitz continuous and Hölder ...
Rubio, M.J., M.J. Rubio, Rubio, M.J. [0000-0002-8765-4060], M.A. Hernández, Hernández, M.A. [0000-0001-5478-2958], Hernández, M.A.   +5 more
core   +5 more sources

A semilocal convergence analysis for the method of tangent parabolas [PDF]

Journal of Numerical Analysis and Approximation Theory, 2005
We present a semilocal convergence analysis for the method of tangent parabolas (Euler-Chebyshev) using a combination of Lipschitz and center Lipschitz conditions on the Fréchet derivatives involved.
Ioannis K. Argyros
doaj   +4 more sources

A new semilocal convergence theorem for Newton's method [PDF]

Journal of Computational and Applied Mathematics, 1997
A new semilocal convergence theorem for Newton's method is established for solving a nonlinear equation F(x) = 0, defined in Banach spaces. It is assumed that the operator F is twice Fréchet differentiable, and F″ satisfies a Lipschitz type condition ...
JoséM Gutiérrez, Gutiérrez, J.M. [0000-0002-0434-7250], Gutiérrez, J.M.   +2 more
core   +5 more sources

Semilocal Convergence Domain of a Chandrasekhar Integral Equation [PDF]

Symmetry
In this study, we discuss the semilocal convergence analysis of a fourth-order iterative method in Banach spaces. We assume the Fréchet derivative satisfies the Lipschitz continuity condition, obtains suitable recurrence relations, and determines ...
Arleen Ledesma, Eulalia Martínez, Ledesma, Arleen, Martínez Molada, Eulalia   +3 more
core   +4 more sources

Modification of the Kantorovich assumptions for semilocal convergence of the Chebyshev method

Journal of Computational and Applied Mathematics, 2000
This study obtains two semilocal convergence results for the well-known Chebyshev method, which is a third-order iterative process. The hypotheses required are modifications to the normal Kantorovich ones.
Salanova, M.A., M.A. Hernández, M.A. Salanova, Hernández, M.A. [0000-0001-5478-2958], Hernández, M.A.   +4 more
core   +5 more sources

Semilocal Convergence Theorem for a Newton-like Method

East Asian Journal on Applied Mathematics, 2017
The semilocal convergence of a third-order Newton-like method for solving nonlinear equations is considered. Under a weak condition (the so-calledγ-condition) on the derivative of the nonlinear operator, we establish a new semilocal convergence theorem ...
Lu Liu, Rong-Fei Lin, Ping-Fei Dai, Min-Hong Chen, Qing-Biao Wu   +4 more
core   +3 more sources

Semilocal Convergence Analysis for Inexact Newton Method under Weak Condition [PDF]

Abstract and Applied Analysis, 2012
Under the hypothesis that the first derivative satisfies some kind of weak Lipschitz conditions, a new semilocal convergence theorem for inexact Newton method is presented.
Xiubin Xu, Yuan Xiao, Tao Liu
doaj   +2 more sources

Convergence analysis of iterative compositions in nonlinear modeling: exploring semilocal and local convergence phenomena [PDF]

Journal of Numerical Analysis and Approximation Theory
In this work, a comprehensive analysis of a multi-step iterative composition for nonlinear equation is performed, providing insights into both local and semilocal convergence properties.
Sunil Kumar, Janak Raj Sharma, Ioannis K. Argyros   +2 more
doaj   +2 more sources

Extending the applicability of the local and semilocal convergence of Newton's method

Applied Mathematics and Computation, 2017
We present a local as well a semilocal convergence analysis for Newton's method in a Banach space setting. Using the same Lipschitz constants as in earlier studies, we extend the applicability of Newton's method as follows: local case: a larger radius is
Argyros, Ioannis K, Magreñán, Á. Alberto, Magreñán, Á. Alberto (1)   +2 more
core   +3 more sources