Projection operators on piecewise polynomial spaces
Ada Cammilleri, Eduardo P. Serrano · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2003
We propose an approximation scheme on representation spaces which elements are piecewise polynomial functions, with deficient regularity on a pre-established grid of knots. We characterize these spaces, expose relevant properties and define appropriate bases. We design approximations methods based on orthogonal projections of a given signal, restricted to certain conditions, according with the regularity that is wished. We suggest applications for this procedure in the context of signal processing.