A local convergence theorem for the inexact Newton method at singular points.
A Method for Finding Sharp Error Bounds for Newton's Method Under the Kantorovich Assumptions.
A method for improving the convergence of iteration sequences
A method for obtaining iterative formulas of higer order
A mixed-FEM and BEM coupling for the approximation of the scattering of thermal waves in locally non-homogeneous media
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
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.
A Modified Continuation Method for the Numerical Solution of Nonlinear Two-Point Boundary Value Problems by Shooting Techniques.
A monotone convergence theorem for Newton-like methods using hypotheses on divided differences of order two.
A multi-step iterative method for approximating fixed points of Presić-Kannan operators.
A new approach for finding weaker conditions for the convergence of Newton's method
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.
A new iterative algorithm for the set of fixed-point problems of nonexpansive mappings and the set of equilibrium problem and variational inequality problem.
A new iterative scheme for countable families of weak relatively nonexpansive mappings and system of generalized mixed equilibrium problems.
A new Kantorovich-type theorem for Newton's method
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.
A note on determination of eigenvalues and eigenfunctions of bounded self-adjoint operators
A note on the difference schemes for hyperbolic equations.
A note on the difference schemes for hyperbolic-elliptic equations.
A Note on the Theory of Limit Processes for Solving Finite Equations.