Optimal Error Bounds for Derivatives of Hermite-Birkhoff Interpolation Polynomials

Abstract:

      In this paper, we consider the Hermite-Birkhoff interpolation problem on the interval [0 , 1] .The optimal error bounds obtained by G.Birkhoff and A.Priver for cubic and quintic Hermite interpolation are extented to the most general Birk hoff interpolation case.Our results also contains that of A.K.Varma and G.Ho well, and are the improvements of the estimates of P.G.Ciarlet et al .