discrete splines

Discrete splines (on a uniform grid) were introduced by Mangasarian and Schumaker in %MangasarianSchumaker71 as solutions to certain variational problems. They were treated in detail by Tom Lyche in his Ph.D. Thesis %Lyche75 `Discrete polynomial spline approximation methods'. %

I expressed my view of them in the B-spline survey %Boor76 to the effect that they also make sense for arbitrary grids, being, in effect, the B-spline coefficients of a spline with some knot sequence but expressed as a linear combination of B-splines on a finer knot sequence. %

Lyche gives error bounds for discrete cubic spline interpolation in %Lyche76c . %

Dikshit and Powar discuss `Discrete cubic spline interpolation' in %DikshitPowar82a . %

Rana describes the `Local behaviour of the first difference of a discrete cubic spline' in %Rana90 . %

Rana and Dubey consider the `Local behaviour of the deficient discrete cubic spline interpolator' in %RanaDubey9x .