We prove the weak and strong convergence of the implicit iterative process to a common fixed point of an asymptotically quasi-I-nonexpansive mapping T and an asymptotically quasi-nonexpansive mapping I, defined on a nonempty closed convex subset of a Banach space.

and Applied Analysis 3 It is an interesting problem to extend the above results to a strongly continuous semigroup of nonexpansive mappings and a strongly continuous semigroup of asymptotically nonexpansive mappings. Let S be a strongly continuous semigroup of nonexpansive self-mappings. In 1998 Shioji and Takahashi 11 introduced, in Hilbert space, the implicit iteration

This paper discusses distributed constraint propagation. We propose a generic distributed framework based on the notion of chaotic iteration. We prove correctness and implicit termination of our algorithm that apply to distributed constraint satisfaction problems, and also leads to sig-niicant speed-ups on distributions of constraint satisfaction problems.

In this paper, we demonstrate a complete version of the convergence theory of the modulus-based matrix splitting iteration methods for solving a class of implicit complementarity problems proposed by Hong and Li (Numer. Linear Algebra Appl. 23:629-641, 2016). New convergence conditions are presented when the system matrix is a positive-definite matrix and an [Formula: see text]-matrix, respecti...

We present in this paper an algorithm for meshing implicit surfaces based on the Delaunay triangulation of a point-set adaptively sampled on an implicit surface. To improve the quality of the resulting triangular mesh, we use at each iteration a mesh optimization algorithm with the following objectives: optimizing the connectivity, retrieving the sharp features, regularizing the triangles shape...

We give a recursion-theoretic characterization of the complexity classes NC for k ≥ 1. In the spirit of implicit computational complexity, it uses no explicit bounds in the recursion and also no separation of variables is needed. It is based on three recursion schemes, one corresponds to time (time iteration), one to space allocation (explicit structural recursion) and one to internal computati...

For subsonic flows and upwind-discretized, linearized 1-D Euler equations, the smoothing behavior of multigrid-accelerated point Gauss-Seidel relaxation is analyzed. Error decay by convection across domain boundaries is also discussed. A fix to poor convergence rates at low Mach numbers is sought in replacing the point relaxation applied to unconditioned Euler equations, by locally implicit "ti...

The effect of artificial diffusion schemes on the convergence of an implicit method is investigated. A multigrid code using a symmetric limited positive scheme in conjunction with a lowerupper symmetric-Gauss-Seidel method is developed for viscous compressible flows. The present numerical method is shown to be an effective multigrid driver in three-dimensions. Despite its reasonably fast conver...

Rosenbrock methods are popular for solving stiff initial value problems for ordinary differential equations. One advantage is that there is no need to solve a nonlinear equation at every iteration, as compared with other implicit methods such as backward difference formulas and implicit Runge-Kutta methods. In this paper, we introduce some trust region techniques to control the time step in the...