Selected papers from the 10th international conference 2009 on nonlinear functional analysis and applications, Seoul, Korea, July 27--31, 2009.
Semilocal analysis of equations with smooth operators.
Semilocal convergence for Newton's method on a Banach space with a convergence structure and twice Fréchet differentiable operators.
Sharp Error Bounds for Newton's Process.
Sharp upper global a posteriori error estimates for nonlinear elliptic variational problems
The paper is devoted to the problem of verification of accuracy of approximate solutions obtained in computer simulations. This problem is strongly related to a posteriori error estimates, giving computable bounds for computational errors and detecting zones in the solution domain where such errors are too large and certain mesh refinements should be performed. A mathematical model embracing nonlinear elliptic variational problems is considered in this work. Based on functional type estimates developed...
Signal reconstruction from given phase of the Fourier transform using Fejér monotone methods
The aim is to reconstruct a signal function x ∈ L₂ if the phase of the Fourier transform [x̂] and some additional a-priori information of convex type are known. The problem can be described as a convex feasibility problem. We solve this problem by different Fejér monotone iterative methods comparing the results and discussing the choice of relaxation parameters. Since the a-priori information is partly related to the spectral space the Fourier transform and its inverse have to be applied in each...
Skipping transition conditions in a posteriori error estimates for finite element discretizations of parabolic equations
In this paper we derive a posteriori error estimates for the heat equation. The time discretization strategy is based on a θ-method and the mesh used for each time-slab is independent of the mesh used for the previous time-slab. The novelty of this paper is an upper bound for the error caused by the coarsening of the mesh used for computing the solution in the previous time-slab. The technique applied for deriving this upper bound is independent of the problem and can be generalized to other time...
Smoothing effect and discretization in time to semilinear parabolic equations with nonsmooth data
The purpose of this paper is to derive the error estimates for discretization in time of a semilinear parabolic equation in a Banach space. The estimates are given in the norm of the space for when the initial condition is not regular.
Solution Manifolds and Submanifolds of Parametrized Equations and Their Discretization Errors.
Solvability of the power flow problem in DC overhead wire circuit modeling
Proper traffic simulation of electric vehicles, which draw energy from overhead wires, requires adequate modeling of traction infrastructure. Such vehicles include trains, trams or trolleybuses. Since the requested power demands depend on a traffic situation, the overhead wire DC electrical circuit is associated with a non-linear power flow problem. Although the Newton-Raphson method is well-known and widely accepted for seeking its solution, the existence of such a solution is not guaranteed. Particularly...
Some iterative methods for solving equilibrium problems and optimization problems.
Some remarks about the monotone inclusion for solutions of nonlinear equations by regula-falsi-like methods
First, a result of J. W. Schmidt about the monotone enclosure of solutions of nonlinear equations is generalized. Then an iteration method is considered, which is more effective than other known methods. For this method, monotone enclosure statements are also proved.
Stability and error estimates valid for infinite time, for strongly monotone and infinitely stiff evolution equations
Stability of the Iteration Method for non Expansive Mappings
The general iteration method for nonexpansive mappings on a Banach space is considered. Under some assumption of fast enough convergence on the sequence of (“almost” nonexpansive) perturbed iteration mappings, if the basic method is τ−convergent for a suitable topology τ weaker than the norm topology, then the perturbed method is also τ−convergent. Application is presented to the gradient-prox method for monotone inclusions in Hilbert spaces.
Stable approximations of a minimal surface problem with variational inequalities.
Stable approximations of set-valued maps
Stable discretization methods with external approximation schemes.
Stable evaluation of differential operators and linear and nonlinear multi-scale filtering.
Steepest descent method on a Riemannian manifold: the convex case.
Steffensen Methods for Solving Generalized Equations
2000 Mathematics Subject Classification: 65G99, 65K10, 47H04.We provide a local convergence analysis for Steffensen's method in order to solve a generalized equation in a Banach space setting. Using well known fixed point theorems for set-valued maps [13] and Hölder type conditions introduced by us in [2] for nonlinear equations, we obtain the superlinear local convergence of Steffensen's method. Our results compare favorably with related ones obtained in [11].