A simple approach to cardinal Lagrange and periodic Lagrange splines
The author considers the cardinal spline interpolation problem of finding an element in \(S_ n\) which interpolates to some given function f at the integers Z, where \(s_ n\) is the space of cardinal splines of degree n having (simple) knots at \(-h+Z\), with \(0\leq h<1\). An explicit expression is derived by using a simple approach to the cardinal Lagrange spline as a combination of decreasing null splines and a polynomial correction term near the origin. Many qualitative properties, new and old, are obtained as immediate consequences. The periodic analogue is also discussed. This method is much simpler than the previous work and is readily generalized to cardinal L-splines.
scientific article; zbMATH DE number 4013217