一类新节点集上的 Newman 有理插值逼近

摘要

为了得到在[－1，1]上对非光滑函数｜x｜逼近误差的上界，构造了一组全新的节点集，并证明了基于该节点集的Newman型有理插值算子逼近函数｜x｜的误差上界为e－21＋ε n其中ε为仅依赖n的小正数，可随着n增大任意减小乃至趋于零。该误差上界优于利用Newman节点集所得到的结果。同时通过合理分配节点集在区间上的分布及改进不等式的证明方法，逼近的误差阶可进一步提高。%In order to get the upper bound of the error of approximating the non-smooth function |x|in [-1, 1], a new set of interpolating nodes was constructed.And the order of approximation is e-21+ε n , whereεonly de-pends on n and ε→0 +( n→∞) .This upper bound of error is sharper than the results obtained with Newman nodes.Furthermore, it can be sharpened by improving the method of the inequality proving and the distribution of nodes.