This article is cited in 3 papers

A wavelet refinement algorithms of the first order spline spaces

A. A. Makarov

St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: The goal of this paper is to obtain a wavelet decomposition (wavelet refinement) of the chain of embedded spaces of splines for an arbitrary refinement of a nonuniform grid, and to derive the corresponding decomposition and reconstruction formulas, to construct wavelet decompositions and decomposition and reconstruction algorithms in the case of an infinite flow for a grid on an open interval and a finite flow for a grid on a segment.

Keywords: spline, wavelet, spline wavelet decomposition, reconstruction matrix, decomposition matrix, subdivision scheme.

MSC: 41A15, 65D07, 42C40, 65T60

Received: 11.10.2011
Accepted: 29.11.2011