Abstract
In this paper we present and analyze a generalization of the Power p subdivision schemes proposed in [3,12]. The Weighted-Power p schemes are based on a harmonic weighted version of the Power p average considered in [12], and their development is motivated by the desire to generalize the nonlinear analysis in [3,5] to interpolatory subdivision schemes with higher than second order accuracy.
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Amat, S., Dadourian, K., Donat, R., Liandrat, J., Trillo, J.C.: Error bounds for a convexity-preserving interpolation and its limit function. J. Comput. Appl. Math. 211(1), 36–44 (2008)
Amat, S., Dadourian, K., Liandrat, J.: On a nonlinear subdivision scheme avoiding Gibbs oscillations and converging towards C s − functions with s > 1. Math. Comp. 80, 959–971 (2011)
Amat, S., Dadourian, K., Liandrat, J.: Analysis of a class of nonlinear subdivision schemes and associated multiresolution transforms. Adv. Comput. Math. 80, 253–277 (2011)
Amat, S., Donat, R., Liandrat, J., Trillo, J.C.: Analysis of a class of nonlinear subdivision schemes. Applications in Image Processing. Found. Comput. Math., 193–225 (2006)
Amat, S., Donat, R., Liandrat, J., Trillo, J.C.: A fully adaptive multiresolution scheme for image processing. Math. Comput. Modelling 46, 2–11 (2007)
Amat, S., Liandrat, J.: On the stability of the PPH nonlinear multiresolution. Appl. Comput. Harmon. Anal. 18(2), 198–206 (2005)
Aràndiga, F., Donat, R.: Stability through synchronization in nonlinear multiscale transformations. SIAM J. Sci. Comput. 29(1), 265–289 (2007)
Aràndiga, F., Donat, R., Santagueda, M.: (in preparation)
Cavaretta, A.S., Dahmen, W., Micchelli, C.A.: Stationary subdivision. Mem. Am. Math. Soc. 93, 346–349 (1991)
Cohen, A., Dyn, N., Matei, B.: Quasilinear subdivision schemes with applications to ENO interpolation. Appl. Comput. Harmon. Anal. 15, 89–116 (2003)
Conti, C., Horman, K.: Polynomial reproduction for univariate subdivision schemes of any arity. J. Aprox. Theory 163, 413–437 (2011)
Dadourian K.: Schémas de Subdivision, Analyses Multirésolutions non-linéaires. Applications. PhD Thesis, Université de Provence, (2008), http://www.cmi.univ-mrs.fr/~dadouria/these/rapport.pdf
Dadourian, K., Liandrat, J.: Analysis of some bivariate non-linear interpolatory subdivision schemes. Numer. Algor. 48, 261–278 (2008)
Deslauriers, G., Dubuc, S.: Interpolation dyadique. In: Fractals, dimension non entiéres et application, Masson, Paris, pp. 44–45 (1987)
Dyn, N.: Subdivision schemes in computer aided geometric design, vol. 20, pp. 36–104. Oxford University Press, Oxford (1992)
Harten, A.: Multiresolution representation of data: A general framework. SINUM 33(3), 1205–1256 (1996)
Marquina, A.: Local piecewise hyperbolic reconstruction of numerical fluxes for nonlinear scalar conservation laws. SIAM J. Sci. Comput. 15(4), 892–915 (1994)
Marquina, A., Serna, S.: Power ENO methods: a fifth order accurate Weighted Power ENO method. J. Comput. Phys. 117, 632–658 (2004)
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Aràndiga, F., Donat, R., Santágueda, M. (2012). Weighted-Power p Nonlinear Subdivision Schemes. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2010. Lecture Notes in Computer Science, vol 6920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27413-8_7
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DOI: https://doi.org/10.1007/978-3-642-27413-8_7
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