We propose the numerical method defined by xn+1 = xn − λ f(xn − μh(xn)) f ′(xn) , n ∈ N, and determine the control parameter λ and μ to converge cubically. In addition, we derive the asymptotic error constant. Applying this proposed scheme to various test functions, numerical results show a good agreement with the theory analyzed in this paper and are proven using Mathematica with its high-prec...

Tae-Hwa Kim and Hong-Kun Xu [Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Analysis 64(2006)1140-1152 ] proved the strong convergence theorems of modified Mann iterations for asymptotically nonexpansive mappings and semigroups on bounded subset C of a Hilbert space by the CQ iteration method. The purpose of this paper is to mod...

Newton's Method constitutes a nested iteration scheme with the Newton step as the outer iteration and a linear solver of the Jacobian system as the inner iteration. We examine the interaction between these two schemes and derive solution techniques for the linear system from the properties of the outer Newton iteration. Contrary to inexact Newton methods, our techniques do not rely on relaxed t...

We consider the problem of finding an optimal policy in a Markov decision process that maximises the expected discounted sum of rewards over an infinite time horizon. Since the explicit iterative dynamical programming scheme does not scale when increasing the dimension of the state space, a number of approximate methods have been developed. These are typically based on value or policy iteration...

We present a numerical method for solving the Poisson equation on a nested grid. The nested grid consists of uniform grids having different grid spacing and is designed to cover the space closer to the center with a finer grid. Thus our numerical method is suitable for computing the gravity of a centrally condensed object. It consists of two parts: the difference scheme for the Poisson equation...

Continuation Calculus (CC), introduced by Geron and Geuvers [2], is a simple foundational model for functional computation. It is closely related to lambda calculus and term rewriting, but it has no variable binding and no pattern matching. It is Turing complete and evaluation is deterministic. Notions like “call-by-value” and “call-by-name” computation are available by choosing appropriate fun...

Distributed computing systems are a viable and less expensive alternative to parallel computers. However, concurrent programming methods in distributed systems have not been studied as extensively as for parallel computers. In the past, a variety of dynamic scheduling schemes suitable for loops with independent iterations on heterogeneous computer clusters have been obtained and studied. Howeve...

A general inner-outer iteration for computing extreme eigenpairs of symmetric/positive-definite matrix pencils is proposed. The principle of the method is to produce a sequence of p-dimensional bases {Xk} that converge to a minimizer of a generalized Rayleigh quotient. The role of the inner iteration is to produce an “update” vector by (approximately) minimizing a quadratic model of the Rayleig...

The inherent iteration required in the multidisciplinary design problem allows the design problem to cast as a dynamical system. The iteration in design is a resultant of the two rootfinding problems. The first root-finding problem is in seeking out candidate designs while the second is in optimizing the candidate designs. Viewing the root-finding schema as a dynamical system allows the applica...

The paper presents some approximation methods for the Boltz-mann equation. In the rst part fully implicit discretization techniques for the spatially homogeneous Boltzmann equation are investigated. The implicit equation is solved using an iteration process. It is shown that the iteration converges to the correct solution for the moments of the distribution function as long as the mass conserva...