Generalization of Steffensen's method for operator equations in Banach space
Generalized IFSs on noncompact spaces.
Generalized variational inequalities and associated nonlinear equations
Here we consider the solvability based on iterative algorithms of the generalized variational inequalities and associated nonlinear equations.
Geometric characteristics for convergence and asymptotics of successive approximations of equations with smooth operators
We discuss the problem of characterizing the possible asymptotic behaviour of the iterates of a sufficiently smooth nonlinear operator acting in a Banach space in small neighbourhoods of a fixed point. It turns out that under natural conditions, for the most part of initial approximations these iterates tend to "lie down" along a finite-dimensional subspace generated by the leading (peripherical) eigensubspaces of the Fréchet derivative at the fixed point and moreover the asymptotic behaviour of...
Gradient methods for the construction of Ljusternik-Schnirelmann critical values
High-degree precision decomposition method for an evolution problem.
How to avoid the use of Green's theorem in the Ciarlet-Raviart theory of variational crimes
Identifiability, stability and reconstruction results of sources by interior measurements.
Ill-posed equations with transformed argument.
Implicit predictor-corrector iteration process for finitely many asymptotically (quasi-)nonexpansive mappings.
Improved ball convergence of Newton's method under general conditions
We present ball convergence results for Newton's method in order to approximate a locally unique solution of a nonlinear operator equation in a Banach space setting. Our hypotheses involve very general majorants on the Fréchet derivatives of the operators involved. In the special case of convex majorants our results, compared with earlier ones, have at least as large radius of convergence, no less tight error bounds on the distances involved, and no less precise information on the uniqueness of...
Improving the convergence of iterative methods
The author considers the operator equation . Methods for acceleration of convergence of the iterative process are investigated.
Inclusion Statements for Operator Equations by a Continuity Principle.
Inexact Newton method under weak and center-weak Lipschitz conditions
The paper develops semilocal convergence of Inexact Newton Method INM for approximating solutions of nonlinear equations in Banach space setting. We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis. The results obtained compare favorably with earlier ones in at least the case of Newton's Method (NM). Numerical examples, where our convergence criteria are satisfied but the earlier ones are not, are also explored.
Inexact Newton methods and recurrent functions
We provide a semilocal convergence analysis for approximating a solution of an equation in a Banach space setting using an inexact Newton method. By using recurrent functions, we provide under the same or weaker hypotheses: finer error bounds on the distances involved, and an at least as precise information on the location of the solution as in earlier papers. Moreover, if the splitting method is used, we show that a smaller number of inner/outer iterations can be obtained. Furthermore, numerical...
Inflated mappings for singularities of codimension
Interior proximal method for variational inequalities on non-polyhedral sets
Interior proximal methods for variational inequalities are, in fact, designed to handle problems on polyhedral convex sets or balls, only. Using a slightly modified concept of Bregman functions, we suggest an interior proximal method for solving variational inequalities (with maximal monotone operators) on convex, in general non-polyhedral sets, including in particular the case in which the set is described by a system of linear as well as strictly convex constraints. The convergence analysis of...
Interpolation in Sobolevschen Funktionenräumen.
Inverse differentiability contractors and equations in Banach spaces
Inverse monotonicity and difference schemes of higher order. A summary for two-point boundary value problems.