Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/86050
Authors: 
Protassov, Vladimir
Year of Publication: 
2001
Series/Report no.: 
Tinbergen Institute Discussion Paper 01-045/4
Abstract: 
We consider the univariate two-scale refinement equation.The paper analyzes the correlation between the existence of smoothcompactly supported solutions of this equation and the convergence ofthe corresponding cascade algorithm/subdivision scheme. We introducea criterion that expresses this correlation in terms of mask of theequation. We show that the convergence of subdivision scheme dependson values that the mask takes at the points of its generalizedcycles. This means in particular that the stability of shifts ofrefinable function is not necessary for the convergence of thesubdivision process. This also leads to some results on the degree ofconvergence of subdivision processes and on factorizations ofrefinable functions.
Subjects: 
refinement equations
cascade algorithm
subdivision process
degree of convergence
stability
cycles
tree
Document Type: 
Working Paper

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