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Convergence of Cascade Algorithms in Sobolev Spaces for Perturbed Refinement Masks |
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| Authors: | Di-Rong Chen Gerlind Plonka |
| Affiliation: | a Department of Applied Mathematics, Beijing University of Aeronautics and Astronautics, Beijing, 100083, People's Republic of China, Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei, 445000, People's Republic of China;b Institute of Mathematics, University of Duisburg, D-47048, Duisburg, Germany |
| 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. |
| Keywords: | cascade algorithm Sobolev space joint spectral radius perturbation of refinable functions. |
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