关于一类修正的三角插值多项式

On a Modifying Triangle Interpolation Polynomial

中文关键词:  修正的三角插值多项式  一致收敛  最佳收敛阶

英文关键词:modifing triangle interpolation polynomial  uniform convergence  best convergence order.

中文摘要:

      本文构造出一个以｛θ_ｋ＝ｋ/(ｎ＋１)π｝^ｎ_ｋ＝１为插值节点的ｆ（θ）∈Ｃ_２π且为奇函数的修正的三角插值多项式Ｗ_n（ｆ；ｒ，θ）（ｒ为自然数）．Ｗ_n（ｆ；ｒ，θ）对每个以２π为周期的奇连续函数都能在全实轴上一致地收敛到ｆ（θ）；若ｆ（θ）∈Ｃ^ｊ_２π（０≤ｊ≤ｒ－１）且是奇的，Ｗ_n（ｆ；ｒ，θ）对其收敛阶均达到最

英文摘要:

      The paper introduces a modifing triangle interpolation polynomial W_n(f;r,θ) (where r is a given natural number) based on these values of f(θ) (where f(θ)∈C_2π and f(θ) is an odd function) on these nodes {θ_k=k/(n+1)π}ⁿ_k=1. W_n(f;r,θ) uniformly converges to f(θ)(f(θ)∈C_2π and f(θ) is an odd function) on the total real axis. The approximation order of W_n(f;r,θ) reaches the best approximation order when used to approximate to f(θ) where f(θ)∈C^j_2π(0≤ j ≤ r - 1) and f (θ) is an odd function.