On the quality of algorithms based on spline interpolation
Let \(C^*\) denote the space of real valued \(n\)-periodic continuous functions endowed with the sup-norm, and let \(I\) be a continuous linear functional on \(C^*\). The paper is devoted to the approximate computation of \(I[f]\) using as input only the function values \(f(j)\), \(j=1, \dots,n\), and the supplementary information \(|f^{(r)}|\leq 1\), where \(r\) is fixed. The quality \(q\) of a numerical algorithm for the computation of \(I[f]\) is defined as the ratio of its error to the smallest possible error of an algorithm based on the same information. It is shown that \(q\) is rather small if the algorithm is based on periodic spline interpolation.
scientific article; zbMATH DE number 993903
scientific article