摘要
讨论了以第二类 Ｔｃｈｅｂｙｃｈｅｆｆ多项式的零点为插值结点纽的 Ｇｒǖｎｗａｌｄ 插值于Ｌｐ下 的收敛性．当１≤ｐ＜２时，给出了收敛速度的一个精确估计；当Ｐ≥２时，说明了其于Ｌｐ下不 是收敛算子列．给出了一种以第二类Ｔｃｈｅｂｙｃｈｅｆｆ多项式的零点为插值结点组的修改的 Ｇｒｕｎｗａｌｄ插值，证明了其于 Ｌｐ（１≤ｐ＜∞）下是收敛的．
The Lp-convergence properties of the Grǖnwald process based on the second kind Tchebycheff nodes are discussed.When1≤p < 2 ,an accurate bound of first convergence rate is given.When p≥2 ,that they aren't Lp,-convergenceo perators sequence is shown. We also give a kind of modified Grunwald process based on the second kind Tchebycheff nodes,and we discuss first Lp-convergence properities for 1≤P<∞
