一个偶三角插值多项式的改进

Improvement of an Even Trigonometric Interpolation Polynomial

对一个偶三角插值多项式算子进行了改进,使其对每个连续偶函数f(x)∈C2π都能在全实轴上一致收敛,并且若f(x)∈Cj2π(0≤j≤r-1)是偶的,则其收敛阶均可达到最佳.

In this paper, an even trigonometric polynomial operator is improved as L_n(f;r,x)(where r is a given natural number), uniformly converges to f(x) on the total real axis ( where f(x)∈C_(2π) and f(x) is an even function).And L_n(f;r,x) reaches the best approximation order when the operator is used to approximate to the even function f(x), where f(x)∈C^j_(2π)(0≤j≤r-1).