Convergence Analysis of the General Gauss-Newton Algorithm.
Convergence conditions for Secant-type methods
We provide new sufficient convergence conditions for the convergence of the secant-type methods to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses recurrent functions, and Lipschitz-type and center-Lipschitz-type instead of just Lipschitz-type conditions on the divided difference of the operator involved. It turns out that this way our error bounds are more precise than earlier ones and under our convergence hypotheses we can cover cases where earlier conditions...
Convergence of Newton-Like Methods for Solving Systems of Nonlinear Equations.
Convergence of Newton-Like-Iterative Methods.
Convergence of sequential and asynchronous nonlinear paracontractions.
Convergence of Stirling's Method in Banach Spaces.
Convergence of the Multigrid Full Approximation Scheme for a Class of Elliptic Mildly Nonlinear Boundary Value Problems.
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.
Determining zeroes of increasing Lipschitz functions.
Die Berechnungskomplexität von elementarsymmetrischen Funkit
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.
Distance entre les racines d'un polynôme
Dualraum und Topologie der (lokal) langsam wachsenden Nullösungen hypoelliptischer Differentialoperatoren.
Effective methods for computing turning points of curves implicitly defined by nonlinear equations
Efficient algorithms for solving nonlinear Volterra integro-differential equations with two point boundary conditions.