余弦函数型最佳一致逼近多项式

依据最佳一致逼近的基本理论,围绕切比雪夫多项式的特征方程,参照余弦函数的变化图形,建立了余弦函数型最佳一致逼近Cn(x)多项式.@@文中介绍了Cn(x)多项式在被逼近函数y(x)=0条件下依据的微分方程、相关定义、有关性质、数学表式、递推公式;讨论了它与切比雪夫Tn(x)多项式之间的关系及转化;提供了在y(x)≠0条件下Cn(x)多项式转化成c(x)所具有的特征和特点;给出了关于c(x)多项式得以实现的具体算法.应用实例表明,在减少多项式的摆动性、提高逼近精度、增大预测范围方面都有较大的改善和提高.

THE BEST UNIFORM APPROXIMATION POLYNOMIAL OF COSINE FUNCTION TYPE

Based on the best uniform approximation theory, centering on chebyshev polynomial characteristic equation, reference cosine function change graph, the Best Uniform Approximation polynomial of Cosine function type is built.
Cn（x） polynomial under the condition of y（x） = 0, basis of differential equations, the definitions, the properties, the appropriate mathematical expressions and the recursive formula, the transformation and relationship between Cn （x） polynomial and Tn（x） polynomial, are
provided.
c（x） polynomial, transformed by Cn（x） under the condition of y（x）≠0, its new characteristics and characteristic , an algorithm of c（x）polynomial to achieve, are presented.
The application example shows that, in reduced polynomial of swing, improving the accuracy of approximation, increasing forecast range, have greatly improved and enhanced.