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Volume 7, Issue 2
On a Nonlinear 4-Point Ternary and Interpolatory Multiresolution Scheme Eliminating the Gibbs Phenomenon

S. Amat, K. Dadourian & J. Liandrat

Int. J. Numer. Anal. Mod., 7 (2010), pp. 261-280.

Published online: 2010-07

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  • 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.

  • Keywords

Nonlinear ternary subdivision scheme, regularity, nonlinear multiresolution, stability, Gibbs phenomenon, signal processing.

  • AMS Subject Headings

41A05, 41A10, 65D05, 65D17

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-7-261, author = {S. Amat, K. Dadourian and J. Liandrat}, title = {On a Nonlinear 4-Point Ternary and Interpolatory Multiresolution Scheme Eliminating the Gibbs Phenomenon}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {2}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/719.html} }
TY - JOUR T1 - On a Nonlinear 4-Point Ternary and Interpolatory Multiresolution Scheme Eliminating the Gibbs Phenomenon AU - S. Amat, K. Dadourian & J. Liandrat JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 261 EP - 280 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/719.html KW - Nonlinear ternary subdivision scheme, regularity, nonlinear multiresolution, stability, Gibbs phenomenon, signal processing. AB -

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.

S. Amat, K. Dadourian and J. Liandrat. (2010). On a Nonlinear 4-Point Ternary and Interpolatory Multiresolution Scheme Eliminating the Gibbs Phenomenon. International Journal of Numerical Analysis and Modeling. 7 (2). 261-280. doi:
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