BLOCK BASED NEWTON-LIKE BLENDING OSCULATORY RATIONAL INTERPOLATION

With Newton＇s interpolating formula, we construct a kind of block based Newton-like blending osculatory interpolation.The interpolation provides us many flexible interpolation schemes for choices which include the expansive Newton＇s polynomial inter- polation as its special case. A bivariate analogy is also discussed and numerical examples are given to show the effectiveness of the interpolation.

Research on the maximum power point tracking method of photovoltaic based on Newton interpolation-assisted particle swarm algorithm

Solar energy has attracted a lot of attention because it is clean and has no pollution.However,due to the partially shaded condition,the photovoltaic array cannot work uniformly at the maximum power point,resulting in a large power loss.To improve this problem,the research of the maximum power point tracking(MPPT)algorithm is discussed by scholars.In this paper,an improved particle swarm optimization(PSO)algorithm is proposed to achieve the goal of MPPT,which uses Newton interpolation-assisted conventional PSO.After tracking to the maximum power point,the Newton interpolation method is used to calculate the maximum power point,reduce the number of iterations of the conventional PSO algorithm and reduce the steady-state oscillation.The simulation is carried out in MATLAB^(■)/Simulink^(■)and compared with conventional PSO.The results show that the improved PSO has better tracking ac-curacy and speed than the conventional algorithm,and the initial tracking speed is increased by>30%.

Novel Investigation of Stochastic Fractional Differential Equations Measles Model via the White Noise and Global Derivative Operator Depending on Mittag-Leffler Kernel

Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.

Prediction of the Aging of HTV Silicone Rubber Using Chemical Concentration and Polynomial Interpolation Approach

Predicting the lifetime of polymeric insulators is one of the most important research topics in studying the life cycle of high voltage insulators in the power transmission and distribution networks. HTV （high temperature vulcanized） silicone rubber is a high performance dielectric material used within electrical power equipment, in particular transmission and distribution insulators. In this paper, we proposed a new approach using the Newton＇s method and Lagrange method to predict the aging of HTV silicone rubber that are subjected to multiple stress conditions. Concentration of chemical elements such as carbon, oxygen, silicon and aluminum were obtained and evaluated using a SEM （scanning electron microscope） with EDS （energy dispersive X-ray spectroscopy）. Curve fitting using the Newton＇s and Lagrange interpolation methods yield useful linear interpolation equations that describe the aging characteristic of the specimens under study. This approach can be applied to predict the change in chemical concentration of polymeric insulators over the life cycle with good accuracy.

Interpolation Method Research and Precision Analysis of GPS Satellite Position

According to the precise ephemeris has only provided satellite position that is discrete not any time,so propose that make use of interpolation method to calculate satellite position at any time.The essay take advantage of IGS precise ephemeris data to calculate satellite position at some time by using Lagrange interpolation,Newton interpolation,Hermite interpolation,Cubic spline interpolation method,Chebyshev fitting method respectively,which has a deeply analysis in the precision of five interpolations. The results show that the precision of Cubic spline interpolation method is the worst,the precision of Chebyshev fitting is better than Hermite interpolation method. Lagrange interpolation and Newton interpolation are better than other methods in precision. Newton interpolation method has the advantages of high speed and high precision. Therefore,Newton interpolation method has a certain scientific significance and practical value to get the position of the satellite quickly and accurately.

ON THE DIVIDED DIFFERENCE FORM OF FAA DI BRUNO＇S FORMULA

The n-divided difference of the composite function h ：= f o g of functions f, g at a group of nodes t0,t1,…,tn is shown by the combinations of divided differences of f at the group of nodes g（t0）,g（t1）,…,g（tm） and divided differences of g at several partial group of nodes t0,t1,…,tn, where m = 1,2,…,n. Especially, when the given group of nodes are equal to each other completely, it will lead to Faà di Bruno＇s formula of higher derivatives of function h.

ON THE DIVIDED DIFFERENCE FORM OF FAA DI BRUNO＇S FORMULA Ⅱ

In this paper, we consider the higher divided difference of a composite function f（g（t）） in which g（t） is an s-dimensional vector. By exploiting some properties from mixed partial divided differences and multivariate Newton interpolation, we generalize the divided difference form of Faà di Bruno＇s formula with a scalar argument. Moreover, a generalized Faà di Bruno＇s formula with a vector argument is derived.

A Criterion for Existence of Bivariate Vector Valued Rational Interpolants

In this paper,a necessary and sufficient condition for the existence of a kind of bivariate vector valued rational interpolants over rectangular grids is given.This criterion is an algebraic method,i.e.,by solving a system of equations based on the given data,we can directly test whether the relevant interpolant exists or not.By coming up with our method, the problem of how to deal with scalar equations and vector equations in the same system of equations is solved.After testing existence,an expression of the corresponding bivariate vector-valued rational interpolant can be constructed consequently.In addition,the way to get the expression is different from the one by making use of Thiele-type bivariate branched vector-valued continued fractions and Samelson inverse which are commonly used to construct the bivariate vector-valued rational interpolants.Compared with the Thiele-type method,the one given in this paper is more direct.Finally,some numerical examples are given to illustrate the result.

A Two-Dimensional Improvement for Farr-Gao Algorithm

Farr-Gao algorithm is a state-of-the-art algorithm for reduced Gr?bner bases of vanishing ideals of finite points, which has been implemented in Maple as a build-in command. This paper presents a two-dimensional improvement for it that employs a preprocessing strategy for computing reduced Gr?bner bases associated with tower subsets of given point sets. Experimental results show that the preprocessed Farr-Gao algorithm is more efficient than the classical one.