Iterative Methods and Applications

Weighted Iterative Operator-Splitting Methods and Applications

The subject of our research is to solve accurately ODEs, which appear in mathematical models arising from several physical processes. For this purpose we develop a new class of weighted iterative operator splitting methods. We present applications to systems of linear ODEs, which might contain also stiff parameters. The benefit of the proposed method is demonstrated with regard to convergence r...

Survey on Geometric Iterative Methods with Applications

Geometric iterative method, also called progressive-iterative approximation (PIA), is an iterative method with clear geometric meaning. Just by adjusting the control points of curves or surfaces iteratively, the limit curve or surface will interpolate (approximate) the given data point set. In this paper, we introduce the geometric iterative method in two aspects, i.e., theory and application. ...

Sequential Methods and Their Applications

Weights in block iterative methods

In this paper we introduce a sequential block iterative method and its simultaneous version with op-timal combination of weights (instead of convex combination) for solving convex feasibility problems.When the intersection of the given family of convex sets is nonempty, it is shown that any sequencegenerated by the given algorithms converges to a feasible point. Additionally for linear feasibil...

Iterative Methods for Approximation of Fixed Points and Their Applications

In this article, we deal with iterative methods for approximation of fixed points and their applications. We first discuss fixed point theorems for a nonexpansive mapping or a family of nonexpansive mappings. In particular, we state a fixed point theorem which answered affirmatively a problem posed during the Conference on Fixed Point Theory and Applications held at CIRM, Marseille-Luminy, 1989...