Newton’s method and its variants are among the most efficient methods known for solving systems of non-linear equations when the functions involved are continuously differentiable. Besides its practical applications, Newton’s method is also a powerful theoretical tool. Therefore, it has been studied and used extensively. One of the famous results on Newton’s method is the well-known Kantorovich...

The notions of Lipschitz conditions with L average are introduced to the study of convergence analysis of Gauss-Newton’s method for singular systems of equations. Unified convergence criteria ensuring the convergence of Gauss-Newton’s method for one kind of singular systems of equations with constant rank derivatives are established and unified estimates of radii of convergence balls are also o...

Wind speed as well as the power output of wind turbine generators (WTGs) have high correlations and may not be normally distributed. In this paper, the method of Zhao’s point estimate method (PEM) combined with Nataf transformation was applied into correlated probabilistic load flow (PLF) calculation. This method can deal with correlated input random variables (RVs) with normal or non-normal pr...

This paper analyzes the behavior of Hong’s point estimate method to account for uncertainties in probabilistic energy management systems to optimize the operation of a microgrid (MG). These uncertainties may arise from different sources, such as the market prices, load demands, and electric power generation of wind farms and photovoltaic systems. Point estimate methods constitute a remarkable t...

A Bayesian analysis is used to detect a change-point in a sequence of independent random variables from exponential distributions. In This paper, we try to estimate change point which occurs in any sequence of independent exponential observations. The Bayes estimators are derived for change point, the rate of exponential distribution before shift and the rate of exponential distribution after s...

This article develops a method of ratio estimate in fuzzy sense. By both the simple random sampling and stratified random sampling, we can obtain the ratio estimate in usual statistical sense. However, the sampling data may be ambiguous in some uncertain circumstance. To solve such kind of problem, we probe into the simple random sampling and stratified random sampling in fuzzy sense, obtain th...

in this paper, a parameter uniform numerical method based on shishkin mesh is suggested to solve a system of second order singularly perturbed differential equations with a turning point exhibiting boundary layers. it is assumed that both equations have a turning point at the same point. an appropriate piecewise uniform mesh is considered and a classical finite difference scheme is applied on t...

Change point estimation is as an effective method for identifying the time of a change in production and service processes. In most of the statistical quality control literature, it is usually assumed that the quality characteristic of interest is independently and identically distributed over time. It is obvious that this assumption could be easily violated in practice. In this paper, we use m...