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- Publisher
- Springer Journals
- Copyright
- Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
- Subject
- Mathematics; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics; Mathematical and Computational Biology; Computational Science and Engineering; Visualization
- ISSN
- 1019-7168
- eISSN
- 1572-9044
- DOI
- 10.1007/s10444-018-9612-x
- Publisher site
- See Article on Publisher Site
Abstract
When a subdivision scheme is factorised into lifting steps, it admits an in–place and invertible implementation, and it can be the predictor of many multiresolution biorthogonal wavelet transforms. In the regular setting where the underlying lattice hierarchy is defined by ℤ s and a dilation matrix M, such a factorisation should deal with every vertex of each subset in ℤ s /Mℤ s in the same way. We define a subdivision scheme which admits such a factorisation as being uniformly elementary factorable. We prove a necessary and sufficient condition on the directions of the Box spline and the arity of the subdivision for the scheme to admit such a factorisation, and recall some known keys to construct it in practice.
Journal
Advances in Computational Mathematics – Springer Journals
Published: Jun 5, 2018