In this note, we introduce a new algorithm to deal with finite dimensional clustering with errors in variables. The design of this algorithm is based on recent theoretical advances (see Loustau (2013a,b)) in statistical learning with errors in variables. As the previous mentioned papers, the algorithm mixes different tools from the inverse problem literature and the machine learning community. ...

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...

The purpose of this paper is to study the weak and strong convergence of an implicit iteration process to a common fixed point for a finite family of nonexpansive nonself-mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of [Xu and Ori, Numer. Funct. Anal. optim. 22(2001) 767-773; Zhou and Chang, Numer. Fund. Anal. Optim. 23(2002) 911-92...

Combining these three definitions, Zamfirescu [12] proved the following important result. Theorem 1.1. Let (X ,d) be a complete metric space and T : X → X a mapping for which there exists the real numbers a,b, and c satisfying a∈ (0,1), b,c ∈ (0,1/2) such that for each pair x, y ∈ X , at least one of the following conditions holds: (z1) d(Tx,Ty)≤ ad(x, y), (z2) d(Tx,Ty)≤ b[d(x,Tx) +d(y,Ty)], (z...

PSIDE is a code for solving implicit differential equations on parallel computers. It is an implementation of the four-stage Radau IIA method. The nonlinear systems are solved by a modified Newton process, in which every Newton iterate itself is computed by an iteration process. This process is constructed such that the four stage values can be computed simultaneously. We describe here how PSID...

We establish a general theorem to approximate common fixed points of quasi-contractive operators on a normed space through the modified Ishikawa iteration process with errors in the sense of Liu [8]. Our result generalizes and improves upon, among others, the corresponding result of Berinde [1]. 2000 Mathematical Subject Clasification: Primary 47H10, 47H17: Secondary 54H25

We establish a general theorem to approximate fixed points of Ćirić quasi-contractive operators on a normed space through the Mann iteration process with errors in the sense of Xu [10]. Our result generalizes and improves upon, among others, the corresponding results of [1,8].

We establish a general theorem to approximate fixed points of Ciric quasi-contractive operators on a generalized convex metric space through the Mann type iteration process with errors in the sense of Xu [11]. Our result generalizes and improves upon, among others, the corresponding results of [1, 8]. 2000 Mathematical Subject Classification: Primary 47H10, 47H17: Secondary 54H25

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...