The stability of subdivision operator at its fixed point

Vladimir Protassov

No EI 2001-03, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: The paper analysis the correlation between the existence of smooth compactly supported solutions of the univariate two-scale refinement equation and the convergence of the corresponding cascade lgorithm/subdivision scheme. We introduce a criterion that expresses this correlation in terms of mask of the equation. We show that the convergence of subdivision scheme depends on values that the mask takes at the points of its generalized cycles. This means in particular that the stability of shifts of refinable function is not necessary for the convergence of the subdivision process. This also leads to some results on the degree of convergence of subdivision processes and on factorizations of refinable functions.

Keywords: cascade algorithm; cycles; degree of convergence; refinement equations; stability; subdivison process; tree (search for similar items in EconPapers)
Date: 2001-01-29
References: Add references at CitEc
Citations:

Downloads: (external link)
https://repub.eur.nl/pub/1668/feweco20010129161126.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ems:eureir:1668

Access Statistics for this paper

More papers in Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute Contact information at EDIRC.
Bibliographic data for series maintained by RePub ( this e-mail address is bad, please contact ).