A local convergence theorem for the inexact Newton method at singular points.
Displaying 21 – 40 of 123
A Method for Finding Sharp Error Bounds for Newton's Method Under the Kantorovich Assumptions.
Tetsuro Yamamoto (1986)
Numerische Mathematik
A method for improving the convergence of iteration sequences
Ivo Marek (1961)
Commentationes Mathematicae Universitatis Carolinae
A method for obtaining iterative formulas of higer order
B. Jovanović (1972)
Matematički Vesnik
A mixed-FEM and BEM coupling for the approximation of the scattering of thermal waves in locally non-homogeneous media
María-Luisa Rapún, Francisco-Javier Sayas (2006)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
This paper proposes and analyzes a BEM-FEM scheme to approximate a time-harmonic diffusion problem in the plane with non-constant coefficients in a bounded area. The model is set as a Helmholtz transmission problem with adsorption and with non-constant coefficients in a bounded domain. We reformulate the problem as a four-field system. For the temperature and the heat flux we use piecewise constant functions and lowest order Raviart-Thomas elements associated to a triangulation approximating the...
A mixed-FEM and BEM coupling for the approximation of the scattering of thermal waves in locally non-homogeneous media
María-Luisa Rapún, Francisco-Javier Sayas (2007)
ESAIM: Mathematical Modelling and Numerical Analysis
This paper proposes and analyzes a BEM-FEM scheme to approximate a time-harmonic diffusion problem in the plane with non-constant coefficients in a bounded area. The model is set as a Helmholtz transmission problem with adsorption and with non-constant coefficients in a bounded domain. We reformulate the problem as a four-field system. For the temperature and the heat flux we use piecewise constant functions and lowest order Raviart-Thomas elements associated to a triangulation approximating the...
A modification of the Kantorovich conditions for the secant method.
Hernández, M.A., Rubio, M.J. (2001)
Southwest Journal of Pure and Applied Mathematics [electronic only]
A Modified Continuation Method for the Numerical Solution of Nonlinear Two-Point Boundary Value Problems by Shooting Techniques.
P. Deuflhard, H.J. Pesch, P. Rentrop (1976)
Numerische Mathematik
A monotone convergence theorem for Newton-like methods using hypotheses on divided differences of order two.
Argyros, Ioannis K. (1999)
Southwest Journal of Pure and Applied Mathematics [electronic only]
A multi-step iterative method for approximating fixed points of Presić-Kannan operators.
Păcurar, M. (2010)
Acta Mathematica Universitatis Comenianae. New Series
A new approach for finding weaker conditions for the convergence of Newton's method
Ioannis K. Argyros (2005)
Applicationes Mathematicae
The Newton-Kantorovich hypothesis (15) has been used for a long time as a sufficient condition for convergence of Newton's method to a locally unique solution of a nonlinear equation in a Banach space setting. Recently in [3], [4] we showed that this hypothesis can always be replaced by a condition weaker in general (see (18), (19) or (20)) whose verification requires the same computational cost. Moreover, finer error bounds and at least as precise information on the location of the solution can...
A new convergence theorem for Steffensen's method on Banach spaces and applications.
Argyros, Ioannis K. (1997)
Southwest Journal of Pure and Applied Mathematics [electronic only]
A new iterative algorithm for the set of fixed-point problems of nonexpansive mappings and the set of equilibrium problem and variational inequality problem.
Kangtunyakarn, Atid (2011)
Abstract and Applied Analysis
A new iterative scheme for countable families of weak relatively nonexpansive mappings and system of generalized mixed equilibrium problems.
Shehu, Yekini (2010)
Abstract and Applied Analysis
A new Kantorovich-type theorem for Newton's method
Ioannis Argyros (1999)
Applicationes Mathematicae
A new Kantorovich-type convergence theorem for Newton's method is established for approximating a locally unique solution of an equation F(x)=0 defined on a Banach space. It is assumed that the operator F is twice Fréchet differentiable, and that F', F'' satisfy Lipschitz conditions. Our convergence condition differs from earlier ones and therefore it has theoretical and practical value.
A Newton-type method and its application.
Vijesh, V.Antony, Subrahmanyam, P.V. (2006)
International Journal of Mathematics and Mathematical Sciences
A note on determination of eigenvalues and eigenfunctions of bounded self-adjoint operators
Josef Kolomý (1966)
Commentationes Mathematicae Universitatis Carolinae
A note on the difference schemes for hyperbolic equations.
Ashyralyev, A., Sobolevskii, P.E. (2001)
Abstract and Applied Analysis
A note on the difference schemes for hyperbolic-elliptic equations.
Ashyralyev, A., Judakova, G., Sobolevskii, P.E. (2006)
Abstract and Applied Analysis
A Note on the Theory of Limit Processes for Solving Finite Equations.
Veikko Seppäla (1972/1973)
Numerische Mathematik