This paper proposes an implicit surface reconstruction algorithm based on Self-Organising Maps (SOMs). The SOM has the connectivity of a regular 3D grid, each node storing its signed distance from the surface. At each iteration of the basic algorithm, a new training set is created by sampling regularly along the normals of the input points. The main training iteration consists of a competitive ...

and Applied Analysis 3 Lemma 1.1 see 21 . let X be a uniformly convex Banach space. Let b and c be two constants with 0 < b < c < 1. Suppose that {tn} is a sequence in b, c . Let {xn} and {yn} be two sequences in X such that lim sup n→∞ ‖xn‖ ≤ d, lim sup n→∞ ∥ yn ∥ ∥ ≤ d, lim n→∞ ∥ tnxn 1 − tn yn ∥ ∥ d 1.8 hold for some d ≥ 0, then limn→∞‖xn − yn‖ 0. Lemma 1.2 see 26 . Let {an}, {bn}, and {cn} ...

The purpose of this paper is to establish the strong convergence of a implicit iteration process with errors to a common fixed point for a finite family of ψ−uniformly pseudocontractive and ψ−uniformly accretive mappings in real Banach spaces. The results presented in this paper extend and improve the corresponding results of Refs. [3, 7, 12]. The remark at the end is important. 2010 Mathematic...

with kn ≥ 0, rn ≥ 0, kn → 1, rn → 0 n → ∞ , for each x, y ∈ C, n 0, 1, 2, . . . . If kn 1 and rn 0, 1.1 reduces to nonexpansive mapping; if rn 0, 1.1 reduces to asymptotically nonexpansive mapping; if kn 1, 1.1 reduces to asymptotically nonexpansive-type mapping. So, a generalized asymptotically nonexpansive mapping is much more general than many other mappings. Browder 1 introduced the followi...

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 aim of this article is to study an implicit iteration process with errors for a finite family of non-Lipschitzian asymptotically nonexpansive in the intermediate sense mappings in Banach spaces. Also we have established some strong convergence theorems for said scheme to converge to common fixed point. The results presented in this paper extend and improve the corresponding results of [1], ...