关于(0,2)型插值多项式逼近

On Approximation of (0, 2) Type Interpolation Polynomials

设n是偶数,P_(n-1)(x)是Legendre多项式,R_n(f,x)是以(1-x^2)P^(?)_(n-1)(x)的零点为基点的所谓(0,2)型插值多项式。本文构造了两个函数类H_(ω_2),H_(ω_1)~*,研究了R_n(f,x)逼近H_(ω_2),H_(ω_1)~*中函数f(x)的阶,并且验证了所给出的逼近阶是最佳的。

Let R_n(f,x) be (0,2) type interpolation polynomial, which is based on the (?)ero(?) of the polynomial (1-x^2)P′_(n-1)(x), where P_(n-1)(x) is the (n-1) th Iegendre polynomial. In this paper, we studied the degree of approximation by R_n(f,x) in H_ω_2 and H_ω_1^(?), respectively. We also proved that our estimate is essentially best possible.