拉格朗日插值多项式于加权L_p下的收敛逼近阶

AN UPPER BOUND FOR THE RATE OF L p CONVERGENCE OF THE LAGRANGE PROCESS ON THE TCHEBYSHEFF NODES

文［１］［２］证明了以Ｔｃｈｅｂｙｓｈｅｆ多项式的零点为插值结点组的拉格朗日插值多项式于加权Ｌｐ意义下的收敛性，但其是仅对Ｐ≤４证明的．本文给出了一个完整的证明过程，且得到了收敛速度的一个上界估计．

Papers proved the L p convergence of the Lagrange interpolatory processes on the Tchebysheff nodes, but lts proof is only for P≥4. This paper gives a complete proof and obtain an upper bound for the rate of L p convergence of the Lagrange proceses on the Tchebycheff