Convergence of derivatives of optimal nodal splines
In this paper the author studies the problem of convergence of derivatives of optimal nodal splines. Optimal nodal spline interpolants \(Wf\) of order \(m\) which have local support can be used to interpolate a continuous function \(f\) at a set of mesh points. The author provides a set of sufficient conditions for a sequence of locally uniform meshes for the uniform convergence of \(D^jWf\) to \(D^jf\) for \(f\in {\mathcal C}^s\) and \(j=1,2\) \(s<m\). He also gives a bound for \(D^rWf\) with \(s<r<m\). Further he uses optimal nodal spline interpolations for the numerical evaluation of Cauchy principal value integrals.
scientific article; zbMATH DE number 1006711