A note on strong convergence of a modified Halpern's iteration for nonexpansive mappings.
A note on the unique solvability of a class of nonlinear equations.
A parameter choice for Tikhonov regularization for solving nonlinear inverse problems leading to optimal convergence rates
We give a derivation of an a-posteriori strategy for choosing the regularization parameter in Tikhonov regularization for solving nonlinear ill-posed problems, which leads to optimal convergence rates. This strategy requires a special stability estimate for the regularized solutions. A new proof fot this stability estimate is given.
A Perturbed Iterative Method for a General Class of Variational Inequalities
The generalized Wiener-Hopf equation and the approximation methods are used to propose a perturbed iterative method to compute the solutions of a general class of nonlinear variational inequalities.
A Predictor-Corrector Technique for Constrained Least-Squares Regularization.
-properness and fixed point theorems for dissipative type maps.
A quasi-Newton method for solving fixed point problems in Hilbert spaces.
A refined Newton’s mesh independence principle for a class of optimal shape design problems
Shape optimization is described by finding the geometry of a structure which is optimal in the sense of a minimized cost function with respect to certain constraints. A Newton’s mesh independence principle was very efficiently used to solve a certain class of optimal design problems in [6]. Here motivated by optimization considerations we show that under the same computational cost an even finer mesh independence principle can be given.
A remark on recent results for finding zeroes of accretive operators.
A remark on solving large systems of equations in function spaces
In order to save CPU-time in solving large systems of equations in function spaces we decompose the large system in subsystems and solve the subsystems by an appropriate method. We give a sufficient condition for the convergence of the corresponding procedure and apply the approach to differential algebraic systems.
A result on segmenting Jungck–Mann iterates
In this paper, following the concepts in [5, 7], we shall establish a convergence result in a uniformly convex Banach space using the Jungck–Mann iteration process introduced by Singh et al [13] and a certain general contractive condition. The authors of [13] established various stability results for a pair of nonself-mappings for both Jungck and Jungck–Mann iteration processes. Our result is a generalization and extension of that of [7] and its corollaries. It is also an improvement on the result...
A shrinking projection method for generalized mixed equilibrium problems, variational inclusion problems and a finite family of quasi-nonexpansive mappings.
A SOR Acceleration of Self-Adjoint and m-Accretive Splitting Iterative Solver for 2-D Neutron Transport Equation
We present an iterative method based on an infinite dimensional adaptation of the successive overrelaxation (SOR) algorithm for solving the 2-D neutron transport equation. In a wide range of application, the neutron transport operator admits a Self-Adjoint and m-Accretive Splitting (SAS). This splitting leads to an ADI-like iterative method which converges unconditionally and is equivalent to a fixed point problem where the operator is a 2 by 2 matrix...
A strong convergence theorem for a common fixed point of two sequences of strictly pseudocontractive mappings in Hilbert spaces and applications.
A strong convergence theorem for a family of quasi--nonexpansive mappings in a Banach space.
A superquadratic method for solving variational inclusions under weak conditions.
A system of generalized mixed equilibrium problems and fixed point problems for pseudocontractive mappings in Hilbert spaces.
A system of nonlinear operator equations for a mixed family of fuzzy and crisp operators in probabilistic normed spaces.
A Unified Approach for Constructing Fast Two-Step Newton-like Methods.
A unifying convergence analysis of Newton's method for twice Fréchet-differentiable operators
We provide a local as well as a semilocal convergence analysis for Newton's method using unifying hypotheses on twice Fréchet-differentiable operators in a Banach space setting. Our approach extends the applicability of Newton's method. Numerical examples are also provided.