Simultaneous Approximation of Sobolev Classes by Piecewise Cubic Hermite Interpolation  

作　　者：Guiqiao Xu Zheng Zhang 

机构地区：[1]Department of Mathematics,Tianjin Normal University,Tianjin,300387,P.R.China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2014年第3期317-333,共17页高等学校计算数学学报（英文版）

基　　金：supported by the National Natural Science Foundations of China(Grant No.11271263).

摘　　要：For the approximation in L_(p)-norm,we determine the weakly asymptotic orders for the simultaneous approximation errors of Sobolev classes by piecewise cubic Hermite interpolation with equidistant knots.For p=1,∞,we obtain its values.By these results we know that for the Sobolev classes,the approximation errors by piecewise cubic Hermite interpolation are weakly equivalent to the corresponding infinite-dimensional Kolmogorov widths.At the same time,the approximation errors of derivatives are weakly equivalent to the corresponding infinite-dimensional Kolmogorov widths.

关 键 词：Piecewise cubic Hermite interpolation L_(p)-norm simultaneous approximation equidistant knot infinite-dimensional Kolmogorov width 

分 类 号：O17[理学—数学]