|x|在扩展的Chebyshev结点的有理插值

On rational interpolation to|x|at the extended Chebyshev nodes

研究|x|在扩展的Chebyshev结点的有理插值,得到逼近阶为O(1/(nln n)).通过数值计算发现相同逼近阶的误差与结点的密集度、结点所在曲线的凹凸性有关.

In this paper,the rational interpolation of|x|at the extended Chebyshev nodes was studied.That the exact order of approximation is O(1/(nln n))was obtained.Through numerical calculation,it is found that the error of the same approximation order is related to the density of nodes and the concavity and convexity of the curve where the nodes are located.