The stability lobe diagram (SLD) is commonly used to determine the suitable cutting parameters of machining system in order achieve a chatter-free process. An improved full-discretization method (FDM) proposed predict SLD based on hybrid interpolation scheme Newton and Lagrange polynomials. In solve SLD, third-order polynomial employed interpolate state term physical space equation system. Mean...

We study theoretically and numerically trigonometric interpolation on symmetric subintervals of [−π, π], based on a family of Chebyshevlike angular nodes (subperiodic interpolation). Their Lebesgue constant increases logarithmically in the degree, and the associated Fejérlike trigonometric quadrature formula has positive weights. Applications are given to the computation of the equilibrium meas...

An interpolation-based method for computing refrigerant properties which can be used in simulations of vaporcompression air-conditioning equipment is presented. This method uses bicubic functions to interpolate between samples of the Helmholtz energy surface as a function of temperature and density. Three beneficial characteristics of this method are discussed: speed, accuracy, and consistency,...

The cycle index polynomial of a symmetric group is a basic tool in combinatorics and especially in Pólya enumeration theory. It seems irrelevant to numerical analysis. Through Faá di Bruno’s formula, cycle index is connected with numerical analysis. In this work, the Hermite interpolation polynomial is explicitly expressed in terms of cycle index. Applications in Gauss-Turán quadrature formula ...

In this paper we show a family of iterative schemes for solving nonlinear equations with order of convergence 2, by using n+ 1 functional evaluations per step, so these methods are optimal in the sense of the Kung-Traub’s conjecture. The family is obtained by composing n Newton’s steps and approximating the derivative by using Hermite’s interpolation polynomial. Some numerical examples are prov...

In this research, a model for managing the emotional state of customers in commercial bank has been developed using deep convolutional neural network (DCNN) and algorithms distributing conflicting along routes to certain operator, depending on state. order route customer it was necessary develop mathematical target routing based Newton interpolation polynomial. The four classes [angry, happy, n...

We present an eecient version of the Horner scheme for the evaluation of multivariate polynomials and study its stability properties. In particular, we show that the backward error of evaluation is bounded by a quantity that is linear in the total degree of the polynomial, which itself is usually signiicantly smaller than the number of operation involved in the evaluation process. Moreover, we ...

Here φ(x) is a smooth cutoff function that localizes the surface S near some specific y ∈ S. The goal here is to determine the values of p for which M is bounded on L. The earliest work on this subject was done in the case where S is a sphere, when Stein [St1] showed M is bounded on L iff p > n+1 n for n > 1. This was later generalized by Greenleaf [Gr] to surfaces of nonvanishing Gaussian curv...