摘要
研究了[-1,1]上节点集的构造、分布特点和其相应的Newman型有理函数对│x│逼近的收敛性之间的本质性联系.指出了对于在零点附近稠密的节点集,若节点在零点附近分布的稠密度大于Newman型节点集对│x│插值时的情形,那么随着零点附近节点稠密度的不断增大,对│x│的有理插值逼近的收敛性呈现逐渐减弱直至不收敛的变化趋势.
The relation between the distribution of sets of interpolation nodes and the quality of approximation for Newman- type rational function to |x| is studied in this paper. For the sets of interpolation nodes whose density concentrates to zero, we reveal if the distribution of nodes close to zero is denser than that of Newman-type interpolation set, the denser the distribution is, the weaker the convergence of rational approximation to |x| will be.Besides, a special set of nodes is discussed whose density concentrates to zero, but |x| can’t be approximated.
出处
《温州师范学院学报》
2005年第2期24-30,共7页
Journal of Wenzhou Teachers College(Philosophy and Social Science Edition)
关键词
有理逼近
收敛性
分布稠密度
rational approximation
convergence
density of distribution.
