Abstract: The inexact generalized Newton method is an iterative method for solving systems of nonsmooth equations. In this paper, the iterative process with a relative residual control is presented and the conditions for local convergence to a solution are provided. These results can be applied to solve Lipschitz continuous equations under some mild assumptions. Moreover, a globally convergent version of the algorithm with a damped approach based on the Armijo rule is considered. [Copyright &y& Elsevier]
Abstract: According to the hierarchical identification principle, a hierarchical gradient based iterative estimation algorithm is derived for multivariable output error moving average systems (i.e., multivariable OEMA-like models) which is different from multivariable CARMA-like models. As there exist unmeasurable noise-free outputs and unknown noise terms in the information vector/matrix of the corresponding identification model, this paper is, by means of the auxiliary model identification idea, to replace the unmeasurable variables in the information vector/matrix with the estimated residuals and the outputs of the auxiliary model. A numerical example is provided. [ABSTRACT FROM AUTHOR]
Consider the following discrete model of a nonautonomous logistic equation: where and are bounded and In this paper, using some kind of iterative method to the above equation, we establish sufficient conditions that ensure the global attractivity for solutions. The result is an extension of the former work [K. Uesugi, Y. Muroya, E. Ishiwata, On the global attractivity for a logistic equation with piecewise constant arguments, J. Math. Anal. Appl. 294 (2004) 560–580] to the nonautonomous case. [Copyright &y& Elsevier]