We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, ...We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, x）‖ which reflects the influence of the position of the x＇s and ω（f^（r＋1）,δ）j,j = 0, 1,... , s,on the error of approximation.展开更多
Recently Brutman and Passow considered Newman-type rational interpolation to ｜x｜ induced by arbitrary set of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods one ...Recently Brutman and Passow considered Newman-type rational interpolation to ｜x｜ induced by arbitrary set 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 paper we consider the special case where the interpolation nodes are the zeros of the Chebyshev polynomial of the second kind and prove that in this case the exact order of approximation is O（1/n｜nn）展开更多
基金Supported by the National Nature Science Foundation.
文摘We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, x）‖ which reflects the influence of the position of the x＇s and ω（f^（r＋1）,δ）j,j = 0, 1,... , s,on the error of approximation.
基金Supported by the National Nature Science Foundation.
文摘Recently Brutman and Passow considered Newman-type rational interpolation to ｜x｜ induced by arbitrary set 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 paper we consider the special case where the interpolation nodes are the zeros of the Chebyshev polynomial of the second kind and prove that in this case the exact order of approximation is O（1/n｜nn）
