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.
