6533b85afe1ef96bd12b9f47

RESEARCH PRODUCT

Non-periodic Polynomial Splines

Amir AverbuchValery A. ZheludevPekka Neittaanmäki

subject

Box splineComputer scienceZak transformMathematicsofComputing_NUMERICALANALYSISMathematics::Numerical AnalysisMatrix polynomialAlgebraSpline (mathematics)Smoothing splineComputer Science::GraphicsWaveletDegree of a polynomialChebyshev nodesComputingMethodologies_COMPUTERGRAPHICS

description

In this chapter, we outline the essentials of the splines theory. By themselves, they are of interest for signal processing research. We use the Zak transform to derive an integral representation of polynomial splines on uniform grids. The integral representation facilitated design of different generators of spline spaces and their duals. It provides explicit expressions for interpolating and smoothing splines of any order. In forthcoming chapters, the integral representation of splines will be used for the constructions of efficient subdivision schemes and so also for the design spline-based wavelets and wavelet frames.

yearjournalcountryeditionlanguage
2015-08-28
https://doi.org/10.1007/978-3-319-22303-2_4