On a Nonlinear 4-Point Ternary and Interpolatory Multiresolution Scheme Eliminating the Gibbs Phenomenon
Year: 2010
International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 2 : pp. 261–280
Abstract
A nonlinear ternary 4-point interpolatory subdivision scheme is presented. It is based on a nonlinear perturbation of the ternary subdivision scheme studied in Hassan M.F., Ivrissimtzis I.P., Dodgson N.A. and Sabin M.A. (2002): "An interpolating 4-point ternary stationary subdivision scheme", Comput. Aided Geom. Design, 19, 1-18. The convergence of the scheme and the regularity of the limit function are analyzed. It is shown that the Gibbs phenomenon, classical in linear schemes, is eliminated. The stability of the associated nonlinear multiresolution scheme is established. Up to our knowledge, this is the first interpolatory scheme of regularity larger than one, avoiding Gibbs oscillations and for which the stability of the associated multiresolution analysis is established. All these properties are very important for real applications.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2010-IJNAM-719
International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 2 : pp. 261–280
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Nonlinear ternary subdivision scheme regularity nonlinear multiresolution stability Gibbs phenomenon signal processing.