Convergence of cascade algorithms in Sobolev spaces for perturbed refinement masks

Authors:
Di-Rong Chen;Gerlind Plonka
Affiliations:
Department of Applied Mathematics, Beijing University of Aeronautics and Astronautics, Beijing, 100083, People's Republic of China/ and Department of Mathematics, Hubei Institute for Nationalities ...;Institute of Mathematics, University of Duisburg, D-47048 Duisburg, Germany
Venue:
Journal of Approximation Theory
Year:
2002

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Abstract

In this paper, the convergence of the cascade algorithm in a Sobolev space is considered if the refinement mask is perturbed. It is proved that the cascade algorithm corresponding to a slightly perturbed mask converges. Moreover, the perturbation of the resulting limit function is estimated in terms of that of the masks.