Subdivision schemes and refinement equations with nonnegative masks

Authors:
Yang Wang
Affiliations:
School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia
Venue:
Journal of Approximation Theory
Year:
2001

Citing 4
Cited 1

Refinement and subdivision for spaces of integer translates of a compactly supported function

Numerical analysis 1987
Two-scale difference equations I: existence and global regularity of solutions

SIAM Journal on Mathematical Analysis
Two-scale difference equations II. local regularity, infinite products of matrices and fractals

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Convergence of Subdivision Schemes Associated with Nonnegative Masks

SIAM Journal on Matrix Analysis and Applications

Two-direction poly-scale refinability

Computers & Mathematics with Applications

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Abstract

We consider the two-scale refinement equation f(x)=Σn=0N cnf(2x-n) with Σn c2n = Σn c2n+1 = 1 where c0, cN ≠ 0 and the corresponding subdivision scheme. We study the convergence of the subdivision scheme and the cascade algorithm when all cn ≥ 0. It has long been conjectured that under such an assumption the subdivision algorithm converge, and the cascade algorithm converge uniformly to a continuous function, if and only if only if 0 c0, cN S = {n: cn 0} is 1. We prove the conjecture for a large class of refinement equations.