An interpolant defined by subdivision and the analysis of the error

摘要

Given a set of points xi, i=0,…,n on [−1,1] and the corresponding values yi, i=0,…,n of a 2-periodic function y(x), supplied in some way by interpolation or approximation, we describe a simple method that by doubling iteratively this original set, produces in the limit a smooth function. The analysis of the interpolation error is given.We show that if y∈C4 then the error in the p-norm, p=1,2 and ∞ depends on the magnitude of the fourth derivative of the function y(x) and on a function α(x) which is even, concave and bounded on [−1,1].