The approximation problem of unsmooth functions gets more and more attention inrecent years. This paper gives further research in the interpolation of unsmooth function|x|αfrom the selection of interpolation nodes to the error estimation, and gets thefollowing results:1)Constructs kinds of nodes to do rational interpolation to | x | on [?1,1]. Thedistribution of some nodes is"uniform"and the one of the others is concentrated. Studiesthe convergence rate of rational interpolation approximating to | x | based on thesenodes.2) Studies the polynomial interpolation to | x |α. Further proves that whenα= 7 , theconjecture of M.Revers[6] about the convergence rate at the zero of Lagrangeinterpolation polynomial on equidistant nodes to | x |αis right. And obtain the concreteapproximation order of Gru????nwald interpolation polynomial to | x | .
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