用额尔米特插值多项式联合逼近函数及其导数

SIMULTANEOUS APPROXIMATION OF FUNCTIONAND THEIR DERIVATIVES BY HERMITEINTERPOLATION POLYNOMIAL

对基于扩充的混合型Jacobi节点的Hermite插值多项式作为工具同时逼近函数及其导数的问题作了讨论。

If f(x) ∈ C>[-1,1] (p≥3). By H2n+1(f;x) denote the Hermite interpolation poly-nomials based on the extended mixed Jacobi nodes: Xk=cos(k= 1,2, …,n),thenwhere ω(f(p),δ) is the modulus of continuity of||g||1,= max{max|g|,max|g'|}.Specially, if f(p)(x)∈ lipα(0 <α<1), then