### A best approximation property of the generalized spline functions.

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

There are two grounds the spline theory stems from – the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one (where splines are obtained via minimization of some quadratic functionals with constraints). We use the general variational approach called $\mathrm{\mathit{s}\mathit{m}\mathit{o}\mathit{o}\mathit{t}\u210e\mathit{i}\mathit{n}\mathit{t}\mathit{e}\mathit{r}\mathit{p}\mathit{o}\mathit{l}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}}$ introduced by Talmi and Gilat and show that it covers not only the cubic spline and its 2D and 3D analogues but also the well known tension spline (called also spline...

In signal and image processing as well as in numerical solution of differential equations, wavelets with short support and with vanishing moments are important because they have good approximation properties and enable fast algorithms. A B-spline of order $m$ is a spline function that has minimal support among all compactly supported refinable functions with respect to a given smoothness. And recently, B. Han and Z. Shen constructed Riesz wavelet bases of ${L}_{2}\left(\mathbb{R}\right)$ with $m$ vanishing moments based on B-spline...