On the convergence of odd-degree spline interpolation (original) (raw)

This paper investigates the convergence properties of odd-degree spline interpolation. A focus is placed on the behavior of polynomial splines of order k (k > 1) and the linear operation of spline interpolation for functions in Cm−1. The results demonstrate that for various degrees of splines, the approximation norms are bounded independently of the partition used. Additionally, the analysis explores cubic and higher-degree splines, providing comprehensive estimates for their projection properties.