Iterations converging to distinct solutions of some nonlinear operator equations in Banach space.
Iterative algorithms with seminorm-induced oblique projections.
Iterative algorithms with variable coefficients for multivalued generalized -hemicontractive mappings without generalized Lipschitz assumption.
Iterative Einschliessungen von Lösungen nichtlinearer Differentialgleichungen durch Newton-ähnliche Iterationsverfahren
In der vorliegenden Arbeit untersuchen wir monoton einschliessende Newton-ähnliche Iterationsverfahren zur näherungsweisen Lösung verschiedener Klassen vonnichtlinearen Differentialgleichungen. Die behandelten Methoden sind auch für nichtkonvexe Nichtlinearitäten anwendbar. Ferner konstruieren wir einschliessende Startnäherungen für diese Verfahren, so dass wir die Existenz der Lösungen der gegebenen Differentialgleichungen sichern können. Die Konvergenz der Verfahren wird auch für den Fall bewiesen,...
Iterative Lösung gewisser Randwertprobleme und Integralgleichungen
Iterative methods for finding common solution of generalized equilibrium problems and variational inequality problems and fixed point problems of a finite family of nonexpansive mappings.
Iterative methods for -strict pseudo-contractive mappings in Hilbert spaces.
Iterative methods for variational inequalities over the intersection of the fixed points set of a nonexpansive semigroup in Banach spaces.
Iterative schemes for fixed points of relatively nonexpansive mappings and their applications.
Local and semilocal convergence theorems for Newton's method based on continuously Fréchet differentiable operators.
Local convergence analysis of inexact Newton-like methods.
Local convergence for a family of iterative methods based on decomposition techniques
We present a local convergence analysis for a family of iterative methods obtained by using decomposition techniques. The convergence of these methods was shown before using hypotheses on up to the seventh derivative although only the first derivative appears in these methods. In the present study we expand the applicability of these methods by showing convergence using only the first derivative. Moreover we present a radius of convergence and computable error bounds based only on Lipschitz constants....
Local convergence for a multi-point family of super-Halley methods in a Banach space under weak conditions
We present a local multi-point convergence analysis for a family of super-Halley methods of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second Fréchet derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet derivative. Numerical examples are also provided.
Local convergence of inexact Newton methods under affine invariant conditions and hypotheses on the second Fréchet derivative
We use inexact Newton iterates to approximate a solution of a nonlinear equation in a Banach space. Solving a nonlinear equation using Newton iterates at each stage is very expensive in general. That is why we consider inexact Newton methods, where the Newton equations are solved only approximately, and in some unspecified manner. In earlier works [2], [3], natural assumptions under which the forcing sequences are uniformly less than one were given based on the second Fréchet derivative of the operator...
Local convergence of two competing third order methods in Banach space
We present a local convergence analysis for two popular third order methods of approximating a solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given for both methods under the same conditions. A comparison is given between the two methods, as well as numerical examples.
Local convergence theorems for Newton's method from data at one point
We provide local convergence theorems for the convergence of Newton's method to a solution of an equation in a Banach space utilizing only information at one point. It turns out that for analytic operators the convergence radius for Newton's method is enlarged compared with earlier results. A numerical example is also provided that compares our results favorably with earlier ones.
Local convergence theorems of Newton’s method for nonlinear equations using outer or generalized inverses
We provide local convergence theorems for Newton’s method in Banach space using outer or generalized inverses. In contrast to earlier results we use hypotheses on the second instead of the first Fréchet-derivative. This way our convergence balls differ from earlier ones. In fact we show that with a simple numerical example that our convergence ball contains earlier ones. This way we have a wider choice of initial guesses than before. Our results can be used to solve undetermined systems, nonlinear...
Modified Jacobian Newton iterative method: theory and applications.
Monotone operators. A survey directed to applications to differential equations
The paper deals with the existence of solutions of the form with operators monotone in a broader sense, including pseudomonotone operators and operators satisfying conditions and . The first part of the paper which has a methodical character is concluded by the proof of an existence theorem for the equation on a reflexive separable Banach space with a bounded demicontinuous coercive operator satisfying condition . The second part which has a character of a survey compares various types of...
Multilevel Schwarz method for the minimization with constraints of non-quadratic functionals.