We present a new implementation of the almost optimal Circumscribed Ellipsoid (CE) Algorithm for approximating fixed points of nonexpanding functions, as well as of functions that may be globally expanding, however, are nonexpanding/contracting in the direction of fixed points. Our algorithm is based only on function values, i.e., it does not require computing derivatives of any order. We utili...

We propose an approach to solving two-dimensional linear and nonlinear boundary-value problems of statics for shallow shells based on the generalized method finite integral transformations Newton– Kantorovich–Raphson linearization. In case, application is reduced construction two with respect different variables in analyzed domain under assumption that kernels one transformation are transforms ...

Power-flow (PF) solution is a basic and powerful tool in power system analysis. Distribution networks (DNs), compared to transmission systems, have many fundamental distinctions that cause the conventional PF to be ineffective on these networks. This paper presents a new fast and efficient PF method which provides all different models of Distributed Generations (DGs) and their operational modes...

Over the past years there has been considerable interest in statistically optimal reconstruction of cross-sectional images from tomographic data. In particular, a variety of such algorithms have been proposed for maximum a posteriori (MAP) reconstruction from emission tomographic data. While MAP estimation requires the solution of an optimization problem, most existing reconstruction algorithms...

Newton-Raphson State Estimation method using bus admittance matrix remains as an efficient and most popular method to estimate the state variables. Elements of Jacobian matrix are computed from standard expressions which lack physical significance. In this paper, elements of the state estimation Jacobian matrix are obtained considering the power flow measurements in the network elements. These ...

In this paper, we revisit the chaotic number of iterations needed by Newton's method to converge to a root. Here, we consider a simple modified Newton method depending on a parameter. It is demonstrated using polynomiography that even in the simple algorithm the presence and the position of the convergent regions, i.e. regions where the method converges nicely to a root, can be complicatedly a ...

In the area of power system planning and operation, contingency analysis plays an important role. In the present days, on-line security assessment is done by contingency ranking, with the help of various computer software, incorporating iterative method like Newton Raphson power flow for obtaining the magnitudes of different parameters. The motive of contingency ranking is to create a short lis...

The DC operating point of an electronic circuit is conventionally found using the NewtonRaphson method. This method is not globally convergent and can only find one solution of the circuit at a time. In this paper, evolutionary computing methods, including Genetic Algorithms, Evolutionary Programming, Evolutionary Strategies and Differential Evolution are explored as possible alternatives to Ne...

This article considerss a Newton-like method already used by several authors but which has not been thouroughly studied yet. We call it the robust-variance scoring (RVS) algorithm because the main version of the algorithm that we consider replaces minus the Hessian of the loglikelihood used in the 1 Newton-Raphson algorithm by a matrix G which is an estimate of the variance of the score under t...