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
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.