Convergence of the Multilevel Full Approximation Scheme including the V-Cycle.
Convergent algorithms suitable for the solution of the semiconductor device equations
In this paper, two algorithms are proposed to solve systems of algebraic equations generated by a discretization procedure of the weak formulation of boundary value problems for systems of nonlinear elliptic equations. The first algorithm, Newton-CG-MG, is suitable for systems with gradient mappings, while the second, Newton-CE-MG, can be applied to more general systems. Convergence theorems are proved and application to the semiconductor device modelling is described.
Curvature computations on surfaces in -space
Das Einschliessen der Lösung von Gleichungen mittels eines verallgemeinerten Iterationsverfahrens
Das Einschliessen der Lösungen von Gleichungen im Banachraum
Deflation Techniques for the Calculation of Further Solutions of a Nonlinear System.
Discrete evolutions: Convergence and applications
We prove a convergence result for a time discrete process of the form under weak conditions on the function . This result is a slight generalization of the convergence result given in [5].Furthermore, we discuss applications to minimizing problems, boundary value problems and systems of nonlinear equations.
Dualraum und Topologie der (lokal) langsam wachsenden Nullösungen hypoelliptischer Differentialoperatoren.
Efficient algorithms for solving nonlinear Volterra integro-differential equations with two point boundary conditions.
Efficient inexact Newton-like methods with application to problems of the deformation theory of plasticity
Newton-like methods are considered with inexact correction computed by some inner iterative method. Composite iterative methods of this type are applied to the solution of nonlinear systems arising from the solution of nonlinear elliptic boundary value problems. Two main quastions are studied in this paper: the convergence of the inexact Newton-like methods and the efficient control of accuracy in computation of the inexact correction. Numerical experiments show the efficiency of the suggested composite...
Ein lokal überlinear konvergentes Verfahren zur Bestimmung von Rückkehrpunkten implizit definierter Raumkurven.
Eine Bemerkung über Iterationsverfahren.
Eine Methode zur Berechnung sämtlicher Lösungen von Polynomgleichungssystemen.
Epsilon-inflation with contractive interval functions
For contractive interval functions we show that results from the iterative process after finitely many iterations if one uses the epsilon-inflated vector as input for instead of the original output vector . Applying Brouwer’s fixed point theorem, zeros of various mathematical problems can be verified in this way.
Error analysis of the nonlinear multigrid method of the second kind
Error Bounds for Computed Eigenvalues and Eigenvectors.
Error Bounds for Newton's Iterates Derived from the Kantorovich Theorem.
Estimates on the semigroups generated by left invariant operators on Lie groups.
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...
Fast intersection methods for the solution of some nonlinear systems of equations.