Einige Anwendungen der mehrdimensionalen approximationstheorie zur Lösungseinschließung bei Randwertaufgaben
Enlargement Procedure for Resolution of Singularities at Simple Singular Solutions of Nonlinear Equations.
Erratum to “Iterative methods for variational inequalities over the intersection of the fixed points set of a nonexpansive semigroup in Banach spaces”.
Error analysis of high-order splitting methods for nonlinear evolutionary Schrödinger equations and application to the MCTDHF equations in electron dynamics
In this work, the error behaviour of high-order exponential operator splitting methods for the time integration of nonlinear evolutionary Schrödinger equations is investigated. The theoretical analysis utilises the framework of abstract evolution equations on Banach spaces and the formal calculus of Lie derivatives. The general approach is substantiated on the basis of a convergence result for exponential operator splitting methods of (nonstiff) order p applied to the multi-configuration time-dependent...
Error Bounds for Newton's Iterates Derived from the Kantorovich Theorem.
Error bounds for Newton's method under a weak Kantorovich-type hypothesis.
Error bounds for the secant method
Error Bounds of Newton Type Process on Banach Spaces.
Error estimates and step-size control for the approximate solution of a first order evolution equation
Error Estimates for Semidiscrete Galerkin Type Approximations for Semilinear Evolution Equations with Nonsmooth Initial Data.
Error estimates for some quasi-interpolation operators
We derive explicit bounds on the constants in error estimates for two quasi-interpolation operators which are modifications of the “classical” Clément-operator. These estimates are crucial for making explicit the constants which appear in popular a posteriori error estimates. They are also compared with corresponding estimates for the standard nodal interpolation operator.
Error estimates of a numerical method for a class of nonlinear evolution equations
Esquisse d'une théorie décompositionnelle
Exact Bounds for the Solution Branches of Nonlinear Eigenvalue Problems.
Expanding the applicability of two-point Newton-like methods under generalized conditions
We use a two-point Newton-like method to approximate a locally unique solution of a nonlinear equation containing a non-differentiable term in a Banach space setting. Using more precise majorizing sequences than in earlier studies, we present a tighter semi-local and local convergence analysis and weaker convergence criteria. This way we expand the applicability of these methods. Numerical examples are provided where the old convergence criteria do not hold but the new convergence criteria are satisfied....
Extending the applicability of Newton's method using nondiscrete induction
We extend the applicability of Newton's method for approximating a solution of a nonlinear operator equation in a Banach space setting using nondiscrete mathematical induction concept introduced by Potra and Pták. We obtain new sufficient convergence conditions for Newton's method using Lipschitz and center-Lipschitz conditions instead of only the Lipschitz condition used in F. A. Potra, V. Pták, Sharp error bounds for Newton's process, Numer. Math., 34 (1980), 63–72, and F. A. Potra, V. Pták, Nondiscrete...
External approximation of bifurcation problems