关于Hermite-Fejēr插值算子的p方收敛

On square p convergence of Hermite Fejēr interpolation operator

在以第二类Ｃｈｅｂｙｓｈｅｖ多项式Ｕｎ（ｘ）的零点ｘｋ＝ｃｏｓθｋ＝ｃｏｓｋπｎ＋１，（ｋ＝１，２，…，ｎ）为插值节点的条件下，讨论了Ｈｅｒｍｉｔｅ－Ｆｅｊēｒ插值算子在［－１，１］上以（１－ｘ２）１２为权函数的ｐ方收敛问题，得到的收敛阶为Ｏ（１）ｗ１ｎＰ＋Ｂｎｐ｛｝．

Square p convergence of weighted function 1-x 2 in {-1,1} with Hermite Fejēr interpolation operator is discussed.Under the condition that the operator has interpolation nodes which are the zeros of second kind Chebyshev polynomial U n(x).i.e.x k= cos θ k= cos k π n+1 (k=1,2,…,n),a convergence order O(1)w1n p+B n·p  is obtained.