Interpolation by multidimensional periodic splines
Let \(\Lambda\) be a non-degenerate lattice in the Euclidean space \(R^ q\). The author defines the notion of \(\Lambda\)-periodic multidimensional spline function associated to a differential operator of elliptic type and studies the problem of interpolation of \(\Lambda\)-periodic functions by splines of this type. The interpolation process is simply and efficient for numerical purposes. It is proved that any \(\Lambda\)- periodic function in \(R^ q\) can be approximated with a given accuracy by \(\Lambda\)-periodic splines such that the approximation error vanishes at a prescribed finite set of knots.
periodic multidimensional spline function
scientific article; zbMATH DE number 4117136
scientific article