Interpolatory Hermite Spline Wavelets

Hermite-interpolatory subdivision schemes

Stationary interpolatory subdivision schemes for Hermite data that consist of function values and first derivatives are examined. A general class of Hermite-interpolatory subdivision schemes is proposed, and some of its basic properties are stated. The goal is to characterise and construct certain classes of nonlinear (and linear) Hermite schemes. For linear Hermite subdivision, smoothness cond...

Interpolatory and Orthonormal Trigonometric Wavelets

The aim of this paper is the detailed investigation of trigono-metric polynomial spaces as a tool for approximation and signal analysis. Sample spaces are generated by equidistant translates of certain de la Vall ee Poussin means. The diierent de la Vall ee Poussin means enable us to choose between better time-or frequency-localization. For nested sample spaces and corresponding wavelet spaces,...

On interpolatory divergence-free wavelets

We construct interpolating divergence-free multiwavelets based on cubic Hermite splines. We give characterizations of the relevant function spaces and indicate their use for analyzing experimental data of incompressible flow fields. We also show that the standard interpolatory wavelets, based on the Deslauriers-Dubuc interpolatory scheme or on interpolatory splines, cannot be used to construct ...

Fourier transform of Hermite interpolatory subdivision schemes

Quasi-interpolatory and Interpolatory Spline Operators: Some Applications

In this paper we consider quasi-interpolatory spline operators that satisfy some interpolation conditions. We give some applications of these operators constructing approximating integral operators and numerically solving Volterra integral equations of the second kind. We prove convergence results for the constructed methods and we perform numerical examples and comparisons with other spline me...