Journal article

Publication year: 2008

Pages: 5-27

Journal: BIT Numerical Mathematics

Volume number: 48

Issue number: 1

ISSN: 0006-3835

DOI Link: https://doi.org/10.1007/s10543-008-0162-3

Publisher: Springer

Abstract: 
We investigate full rank interpolatory vector subdivision schemes whose masks are positive definite on the unit circle except the point z=1. Such masks are known to give rise to convergent schemes with a cardinal limit function in the scalar case. In the full rank vector case, we show that there also exists a cardinal refinable function based on this mask, however, with respect to a different notion of refinability which nevertheless also leads to an iterative scheme for the computation of vector fields. Moreover, we show the existence of orthogonal scaling functions for multichannel wavelets and give a constructive method to obtain these scaling functions.

Harvard Citation style: Conti, C., Cotronei, M. and Sauer, T. (2008) Full rank positive matrix symbols: Interpolation and orthogonality, BIT Numerical Mathematics, 48(1), pp. 5-27. https://doi.org/10.1007/s10543-008-0162-3

APA Citation style: Conti, C., Cotronei, M., & Sauer, T. (2008). Full rank positive matrix symbols: Interpolation and orthogonality. BIT Numerical Mathematics. 48(1), 5-27. https://doi.org/10.1007/s10543-008-0162-3