Due to the Lagrange interpolation of |x|~αapproximation properties is poor,rational approximation of nonsmooth function| x | is very effective,this paper considers the rational approximation of |x|~α. The Newman-α type rational operator is constructed,it has comonotone properties with |x|~αon(- ∞,+ ∞). Then the convergence rate of the Newman-α type rational operator to |x|~αis considered based on Chebyshev notes of second kind. The exact order of approximation is only O(1n). The result is worse than rationa...
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