Sequential regularization of ill-posed problems involving unbounded 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...
Single step methods for inhomogeneous linear differential equations in Banach space
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 and interpolation in a convex subset of a Hilbert space : II. The semi-norm case
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.
Sobolev type inequalities for p>0
Solution Manifolds and Submanifolds of Parametrized Equations and Their Discretization Errors.
Solution of a finite-dimensional problem with -mappings and diagonal multivalued operators.
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 equilibrium and mixed models in the finite element method
Some functions of eigenvalues of normal operator
Kellogg's iterations in the eigenvalue problem are discussed with respect to the boundary spectrum of a linear normal operator.
Some insights into the regularization of ill-posed problems.
Some iterative methods for solving equilibrium problems and optimization problems.
Some possibilities in solving operator equations using non stationary iterative method
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.
Some remarks on best regularization
Some theorems on the stability of numerical processes
Nell’articolo si dimostrano alcuni teoremi sulla stabilità dei processi numerici di Ritz e della collocazione in rapporto agli errori di «distorsione».