基于修正的第二类Chebyshev结点的Newman型有理插值函数对|x|的逼近

Recently Brutman and Passow considered Newman-type rational interpolation to ｜x｜ induced by arbitrary sets of symmetric nodes in -1,1] and gave the general estimation of the approximation error.By their methods,one could establish the exact order of approximation for some special nodes.In the present note we consider the sets of interpolation nodes obtained by adjusting the Chebyshev roots of the second kind on the interval 0,1] and then extending this set to -1,1] in a symmetric way.We show that in this case the exact order of approximation is O（ 1 n 2 ）.

On Newman-Type Rational Interpolation to |x| at the Adjusted Chebyshev Nodes of the Second Kind

Recently Brutman and Passow considered Newman-type rational interpolation to $|x|$ induced by arbitrary sets of symmetric nodes in $-1,1]$ and gave the general estimation of the approximation error. By their methods, one could establish the exact order of approximation for some special nodes. In the present note we consider the sets of interpolation nodes obtained by adjusting the Chebyshev roots of the second kind on the interval $0,1]$ and then extending this set to $-1,1]$ in a symmetric way. We show that in this case the exact order of approximation is $O(\frac{1}{n^2})$.