On the Approximative Roots of Maximal Monotone Mappings
On the Chaplyghin method for generalized solutions of partial differential functional equations.
On the computation of nonhyperbolic fixed points.
On the Concepts of Convergence, Consistency, and Stability in Connection with some Numerical Methods.
On the convergence and application of Stirling's method
We provide new sufficient convergence conditions for the local and semilocal convergence of Stirling's method to a locally unique solution of a nonlinear operator equation in a Banach space setting. In contrast to earlier results we do not make use of the basic restrictive assumption in [8] that the norm of the Fréchet derivative of the operator involved is strictly bounded above by 1. The study concludes with a numerical example where our results compare favorably with earlier ones.
On the convergence of eigenvalues for mixed formulations
On the convergence of gelerkin approximations
On the convergence of modified relaxation methods for extremum problems
On the convergence of Newton's method for analytic operators.
On the convergence of Newton's method under ω*-conditioned second derivative
We provide a new semilocal result for the quadratic convergence of Newton's method under ω*-conditioned second Fréchet derivative on a Banach space. This way we can handle equations where the usual Lipschitz-type conditions are not verifiable. An application involving nonlinear integral equations and two boundary value problems is provided. It turns out that a similar result using ω-conditioned hypotheses can provide usable error estimates indicating only linear convergence for Newton's method.
On the convergence of perturbed Newton-like methods in Banach space and applications.
On the convergence of semiiterative methods to the Drazin inverse solution of linear equations in Banach spaces.
On the convergence of the secant method under the gamma condition
We provide sufficient convergence conditions for the Secant method of approximating a locally unique solution of an operator equation in a Banach space. The main hypothesis is the gamma condition first introduced in [10] for the study of Newton’s method. Our sufficient convergence condition reduces to the one obtained in [10] for Newton’s method. A numerical example is also provided.
On the convergence of two-step Newton-type methods of high efficiency index
We introduce a new idea of recurrent functions to provide a new semilocal convergence analysis for two-step Newton-type methods of high efficiency index. It turns out that our sufficient convergence conditions are weaker, and the error bounds are tighter than in earlier studies in many interesting cases. Applications and numerical examples, involving a nonlinear integral equation of Chandrasekhar type, and a differential equation containing a Green's kernel are also provided.
On the discretization of a partial differential equation in the neighborhood of a periodic orbit.
On the existence of solutions and one-step method for functional-differential equations with parameters
On the Fast Convergence of a Galerkin-Like Method for Equations of the Second Kind.
On the Global Convergence of Halley's Iteration Formula.
On the Halley method in Banach spaces
We provide a semilocal convergence analysis for Halley's method using convex majorants in order to approximate a locally unique solution of a nonlinear operator equation in a Banach space setting. Our results reduce and improve earlier ones in special cases.
On the iterative process of solving nonlinear operator equations in PTL-spaces