An infeasible interior-point algorithm for solving the$P_*$-matrix linear complementarity problem based on a kernelfunction with trigonometric barrier term is analyzed. Each (main)iteration of the algorithm consists of a feasibility step andseveral centrality steps, whose feasibility step is induced by atrigonometric kernel function. The complexity result coincides withthe best result for infea...

We present a new algorithm obtained by changing the search directions in the algorithm given in [8]. This algorithm is based on a new technique for finding the search direction and the strategy of the central path. At each iteration, we use only the full Nesterov-Todd (NT)step. Moreover, we obtain the currently best known iteration bound for the infeasible interior-point algorithms with full NT...

In this paper, first we use an example to show the efficiency of $M$ iteration process introduced by Ullah and Arshad [4] for approximating fixed points of Suzuki generalized nonexpansive mappings. Then by using $M$ iteration process, we prove some strong and $Delta -$convergence theorems for Suzuki generalized nonexpansive mappings in the setting of $CAT(0)$ Spaces. Our results are the extensi...

This paper will concentrate on contributions of CWI to the development of parallel Runge-Kutta (RK) methods. We shall describe two approaches to construct such methods. In both approaches, a conventional implicit RK method is used as a corrector equation whose solution is approximated by an iterative method. In the first approach, the iteration method uses a fixed number of iterations without s...

SUMMARY Recently the GMRESR inner-outer iteration scheme for the solution of linear systems of equations has been proposed by Van der Vorst and Vuik. Similar methods have been proposed by Axelsson and Vassilevski 1] and Saad (FGMRES) 10]. The outer iteration is GCR, which minimizes the residual over a given set of direction vectors. The inner iteration is GMRES, which at each step computes a ne...

We establish a general theorem to approximate fixed points of quasi-contractive operators on a normed space through the three-step iteration process. Our result generalizes and improves upon, among others, the corresponding result of Berinde [1].