The present paper constructs a set of nodes which can generate a rationalinterpolating function to approximate |x|at the rate of O(1/(nk log n))for any givennatural number κ.More importantly.this construction reveals...The present paper constructs a set of nodes which can generate a rationalinterpolating function to approximate |x|at the rate of O(1/(nk log n))for any givennatural number κ.More importantly.this construction reveals the fact that the higherdensity the distribution of a set of nodes has to zero (that is the singular point of thefunction |x|!),the better the rational interpolation approximation behaves.This probablyalso provides an idea to construct more valuable sets of nodes in the future.展开更多
基金Supported in part by National and Provincial Natural Science Foundations(under grant numbers 10141001 and 101009)by Ningbo Key Doctoral Funds.
文摘The present paper constructs a set of nodes which can generate a rationalinterpolating function to approximate |x|at the rate of O(1/(nk log n))for any givennatural number κ.More importantly.this construction reveals the fact that the higherdensity the distribution of a set of nodes has to zero (that is the singular point of thefunction |x|!),the better the rational interpolation approximation behaves.This probablyalso provides an idea to construct more valuable sets of nodes in the future.
