The solvability of a class of general nonlinear implicit variational inequalities based on perturbed three-step iterative processes with errors.
The waiting time property for parabolic problems trough the nondiffusion of support for the stationary problems.
In this note we study the waiting time phenomenon for local solutions of the nonlinear diffusion equation through its connection with the nondiffusion of the support property for local solutions of the family of discretized elliptic problems. We show that, under a suitable growth condition on the initial datum near the boundary of its support, a finite part of the family of solutions of the discretized problem maintain unchanged its support.
Three remarks on the use of Čebyšev polynomials for solving equations of the second kind
Time discretizations for evolution problems
The aim of this work is to give an introductory survey on time discretizations for liner parabolic problems. The theory of stability for stiff ordinary differential equations is explained on this problem and applied to Runge-Kutta and multi-step discretizations. Moreover, a natural connection between Galerkin time discretizations and Runge-Kutta methods together with order reduction phenomenon is discussed.
Tractability of multivariate problems for weighted spaces of functions
We survey recent results on tractability of multivariate problems. We mainly restrict ourselves to linear multivariate problems studied in the worst case setting. Typical examples include multivariate integration and function approximation for weighted spaces of smooth functions.
T-stability approach to variational iteration method for solving integral equations.
Two step extrapolation and optimum choice of relaxation factor of the extrapolated S.O.R. method
Limits of the extrapolation coefficients are rational functions of several poles with the largest moduli of the resolvent operator and therefore good estimates of these poles could be calculated from these coefficients. The calculation is very easy for the case of two coefficients and its practical effect in finite dimensional space is considerable. The results are used for acceleration of S.O.R. method.
Über die Konvergenzgeschwindigkeit projektiver Verfahren. II.
Über die Optimierung eines zweiparametrigen Iterationsverfahrens
Über eine Näherungsmethode zur Lösung gewisser Randwertaufgaben der Reaktortheorie
Über einige Klassen von Iterationsverfahren in Banach-Räumen.
Über Fehlerabschaetzungen a priori und a posteriori
Über mehrstufige Iterationsverfahren und die Lösung der Hammersteinschen Gleichung.
Über neue iterative Methoden im Eigenwertproblem eines beschränkten linearen Operators
Über schwach zyklische Abbildungen in nichtlinearen Produkträumen und einige Monotonieaussagen
In der Arbeit werden einige Eigenschaften der sog. schwach zyklischen Vektorfunktionen untersucht. Die allgemeine Deffinition einer schwach zyklischen Funktion enthält als einen Spezialfall Funktionen der Form mit einer schwach zyklischen Matrix . Es werden insbesondere Monotonie Eigenschaften schwach zyklischer Funktionen betrachtet, wobei die Monotonie in verallgemeinertem Sinn definiert wird.
Učení neuronových sítí jako inverzní úloha
Un critère de convergence pour des méthodes générales de point fixe
Unconditional stability of difference formulas
The paper concerns the solution of partial differential equations of evolution type by the finite difference method. The author discusses the general assumptions on the original equation as well as its discretization, which guarantee that the difference scheme is unconditionally stable, i.e. stable without any stability condition for the time-step. A new notion of the -acceptability of the integration formula is introduced and examples of such formulas are given. The results can be applied to ordinary...
Une remarque sur l'équation des erreurs dans la solution approximative des équations différentielles
Unified Error Analysis for Newton-Type Methods .