The reconstruction and decomposition matrixes for linear splines

A. A. Makarov

St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: The aim of the paper is construction of calibration relations in the case of class of coordinate non-polynomial splines connected with refinement of grids. An embedding of spline spaces is established for arbitrary refinement of grids. The reconstruction matrixes in the case of a grid on an open interval and a grid on a segment are constructed. The system of biorthogonal linear functionals to splines is constructed. The decomposition matrixes in the case of a grid on an open interval and a grid on a segment are constructed.

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

UDC: 519.6

Received: 08.07.2011
Accepted: 29.09.2011