The issue of convergence has been hotly debated since the mid 1980s. Only recently certain consensus has arisen around some of the most fundamental issues. It seems hardly surprising, then, to find a large variation in how those issues are taught to undergraduates. This paper is an attempt at clarifying the different concepts of convergence, and their relation to both the neoclassical model of ...

In this paper, we prove the global convergence of the Perry-Shanno’s memoryless quasi-Newton (PSMQN) method with a new inexact line search when applied to nonconvex unconstrained minimization problems. Preliminary numerical results show that the PSMQN with the particularly line search conditions are very promising.

We propose a simple and intuitive method to derive the exact convergence rate of global L2-norm error for strong numerical approximation of stochastic differential equations the result of which has been reported by Hofmann and Müller-Gronbach (2004). We conclude that any strong numerical scheme of order γ > 1/2 has the same optimal convergence rate for this error. The method clearly reveals the...

This paper provides a discussion of the consequences of digital convergence on strategic management. In order to show the multiple effects we follow a three-steps approach. First, we investigate the implications on industry structure based on Porters concept of structural analysis of industries. The second step investigates the implications on critical success factors. Finally, we analyze the c...

In this paper, we analyze the global convergence properties of Perry-Shanno memoryless quasiNewton type method associating with a new line search model. preliminary numerical results are also reported.

A detailed study of power series on the Levi-Civita fields is presented. After reviewing two types of convergence on those fields, including convergence criteria for power series, we study some analytical properties of power series. We show that within their domain of convergence, power series are infinitely often differentiable and reexpandable around any point within the radius of convergence...

In this paper, we review recent advances in the approximation of multivariate functions using eigenfunctions of the Laplace operator subject to homogeneous Neumann boundary conditions. Such eigenfunctions are known explicitly on a variety of domains, including the d-variate cube, equilateral triangle and numerous other higher dimensional simplices. Practical construction of truncated expansions...

A family of improved secant-like method is proposed in this paper. Further, the analysis of the convergence shows that this method has super-linear convergence. Efficiency are demonstrated by numerical experiments when the choice of α is correct. Keywords—Nonlinear equations, Secant method, Convergence order, Secant-like method.

Service Oriented Architectures are an abstract concept which exposes capabilities in distributed, domain-spanning environments as services. These modern systems have three characteristics: They are heterogeneous, distributed and loose Coupling. With increasing popularity of Service Oriented Architecture (SOA), this is no longer possible since interacting systems are generally not located within...

Adaptive optimal control of nonlinear dynamic systems with deterministic and known dynamics under a known undiscounted infinite-horizon cost function is investigated. Policy iteration scheme initiated using a stabilizing initial control is analyzed in solving the problem. The convergence of the iterations and the optimality of the limit functions, which follows from the established uniqueness o...