一种拟Grnwald插值算子的加权L_p收敛速度

The rate of weighted L_p convergence of a kind of quasi-Grnwald interpolatory operators

给出了以第二类Chebyshev多项式的零点为插值结点组的一种拟Grnwald插值多项式在加权Lp范数下收敛速度的一个估计,并证明了其在弱渐近阶的意义下是精确的.这个结论说明了拟Gru¨nwald插值算子在加权Lp意义下是收敛算子列.

This paper obtains an upper bound for the rate of weighted Lp convergence of a kind of quasi-Grǖnwald interpolatory polynomials based on the zeros of Chebyshev polynomials of the second kind and this bound is shown to be exact in the sense of weak asymptotic order. The result shows that the sequence of quasi-Grǖnwald interpolation operators is convergent in the sense of weighted Lp norm.