APPROXIMATION PROPERTIES OF LAGRANGE INTERPOLATION POLYNOMIAL BASED ON THE ZEROS OF (1 - x~2)cosnarccosx

摘要

We study some approximation properties of Lagrange interpolation polynomial based on the zeros of (1 - x~2)cos n axccos x. By using a decomposition for f(x) ∈ C~rC~(r+1) we obtain an estimate of ‖f(x)-L_(n+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.