This paper investigates the optimal Lagrange interpolation of a class F∞of infinitely differentiable functions on[-1,1]in L_(∞)[-1,1]and weighted spaces L_(p,ω)[-1,1],1≤p<∞withωa continuous integrable weight ...This paper investigates the optimal Lagrange interpolation of a class F∞of infinitely differentiable functions on[-1,1]in L_(∞)[-1,1]and weighted spaces L_(p,ω)[-1,1],1≤p<∞withωa continuous integrable weight function in(-1,1).We proved that the Lagrange interpolation polynomials based on the zeros of polynomials with the leading coefficient 1 of the least deviation from zero in L_(p,ω)[-1,1]are optimal for 1≤p<∞.We also give the optimal Lagrange interpolation nodes when the endpoints are included in the nodes.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11871006).
文摘This paper investigates the optimal Lagrange interpolation of a class F∞of infinitely differentiable functions on[-1,1]in L_(∞)[-1,1]and weighted spaces L_(p,ω)[-1,1],1≤p<∞withωa continuous integrable weight function in(-1,1).We proved that the Lagrange interpolation polynomials based on the zeros of polynomials with the leading coefficient 1 of the least deviation from zero in L_(p,ω)[-1,1]are optimal for 1≤p<∞.We also give the optimal Lagrange interpolation nodes when the endpoints are included in the nodes.
