, 69 II.3.2.a Résultat de convergence 70 II.3.2.b Résultat de régularité, p.75
, 86 II.4.2.a Un cas particulier: le schéma pph, II.4.2.b Construction des schémas Spowerp et propriétés de la moyenne powerp 89 II.4.2.c Convergence et régularité des schémas, p.92
, 122 II.5.6 Exemples de schémas non-linéaires définis sur l ? (Z 2 ), 123 II.5.6.a Convergence du schéma Spowerp étendu à l ? (Z 2 )b Convergence du schéma Spphapprox étendu à l ? (Z 2 ), p.123
, 139 III.4.1 Un premier exemple: une analyse multirésolution associée au schéma non-linéaire de, Exemples d'analyses multirésolutions stables sur l ?, p.141
, 144 III.4.2.a Construction du schéma, p.147
, 176 IV.3.2.a Construction d'une grille adaptée, p.177
, Tensor product multiresolution analysis with error control for compact image representation, Signal Processing, vol.82, issue.4, pp.587-608, 2002.
DOI : 10.1016/S0165-1684(01)00206-7
, Weighted ENO interpolation and applications, Communications in Nonlinear Science and Numerical Simulation, vol.9, issue.2, pp.187-195, 2004.
DOI : 10.1016/S1007-5704(03)00107-2
, Nonlinear multi-scale decompositions: The approach of a. harten. Numerical Algorithms, pp.175-216, 2000.
, Multiresolution based on weighted averages of the hat function i: Linear reconstruction techniques, SIAM J. Numer. Anal, vol.36, pp.160-203, 1999.
, Multiresolution based on weighted averages of the hat function ii: Non-linear reconstruction techniques, SIAM J. Numer. Anal, vol.20, pp.1053-1093, 1999.
, On a general analysis tool for nonlinear interpolatory subdivision schemes and associated multiresolution transform Advances of Computational Mathematics
, Analysis of a New Nonlinear Subdivision Scheme. Applications in Image Processing, Foundations of Computational Mathematics, vol.6, issue.2, pp.193-226, 2006.
DOI : 10.1007/s10208-004-0122-5
, Non-linear subdivision using local spherical coordinates, Computer Aided Geometric Design, vol.20, issue.3, pp.165-187, 2003.
DOI : 10.1016/S0167-8396(03)00028-1
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.83.454
, On the stability of the PPH nonlinear multiresolution, Applied and Computational Harmonic Analysis, vol.18, issue.2, pp.198-206, 2005.
DOI : 10.1016/j.acha.2004.12.002
, Avances en la multiresolution de Harten y applicaciones, 2001.
, Non-linear Subdivision of univariate signals and discrete surfaces, 2003.
, An interpolatory 4-point c 2 ternary nonstationary subdivision scheme with tension control, Computer Aided Geometric Design, vol.24, pp.210-219, 2007.
, A non-stationary uniform tension controlled interpolating 4-point scheme reproducing conics, Computer Aided Geometric Design, vol.24, issue.1, pp.1-9, 2007.
DOI : 10.1016/j.cagd.2006.10.003
, Weighted eno y aplicaciones, 2004.
, Application of generalized wavelets: an adaptive multiresolution scheme Recursevely generated b-spline surfaces on topological meshes Point value multiscale algorithms for 2d compressible flows, CDF92] A. Cohen, I. Daubechies, and J. C. Feauveau. Biorthogonal bases of compactly supported wavelets. Comm. Pure Appl, pp.275-321350, 1978.
, Stationary subdivision. Memoirs of the, pp.346-349, 1991.
DOI : 10.1090/memo/0453
, Quasilinear subdivision schemes with applications to ENO interpolation, Applied and Computational Harmonic Analysis, vol.15, issue.2, pp.89-116, 2003.
DOI : 10.1016/S1063-5203(03)00061-7
, Uniformly high order accurate essentially non-oscillatory schemes, iii An algorithm for high speed curve generation, Journal of Computational Physics Computer Grpahics and Image Processing, vol.89, issue.3, pp.231-303346, 1974.
, Fully adaptive multiresolution finite volume schemes for conservation laws Weighted essentially non-oscillatory schemes Stationary subdivsion schemes reproducing polynomials A C 2 four-point subdivision scheme with fourth order accuracy and its extensions A four-point interpolatory subdivision scheme for curve design, DD89] G. Delauriers and S. Dubuc. Symmetric iterative interpolation processes. Constructive Appoximation Mathematical Methods for Curves and Surfaces, pp.183-225200, 1987.
, Multiresolution schemes for conservation laws, DGS99] I. Daubechies, I. Guskov, and W. Sweldens. Regularity of iregular subdivision. Constructive Appoximation, pp.381-426, 1998.
DOI : 10.1007/s211-001-8009-3
, Approximation order of interpolatory nonlinear subdivision schemes, Journal of Computational and Applied Mathematics, vol.233, issue.7, 2008.
DOI : 10.1016/j.cam.2009.02.017
, Convexity preservation of the four-point interpolatory subdivision scheme, Computer Aided Geometric Design, vol.16, issue.8, pp.789-792, 1999.
DOI : 10.1016/S0167-8396(99)00019-9
, Analysis of asymptotically equivalent binary subdivision scheme Subdivision schemes in geometric modelling Intrepolating wavelet transforms Normal multi-resolution approximation of curves. Constructive Appoximation Behaviour of recursive division surface near extraordinay points Nonlinear pyramid transforms based on median interpolation [Dyn92] N. Dyn. Subdivision schemes in computer aided geometric design Combinig wavelets with finite differences: a consistence analysis, Journal of Mathematical Analysis end ApplicationsDRS04] I. Daubechies, O. Runborg, and W. Sweldens Floater and C. A. Micchelli. Nonlinear stationary subdivision. Approximation TheoryGro08] P. Grohs. Smoothness analysis of subdivision schemes on regular grids by proximity, pp.594-621, 1978.
, Log-exponential analogues of univariate subdivision schemes in lie groups and their smoothness properties Approximation Theory XII: San Antonio [Har93] A. Harten. eno schemes with subcell resoolution Adaptive multiresolution schemes for shock computations Multiresolution representation of data: a general framework, Journal of Applied Numerical Analysis Journal of Computational Physics SIAM Journal Numerical Analysis, vol.46, issue.33, pp.2169-2182, 1993.
, An interpolating 4-point c 2 ternary stationary subdivsion scheme Stability of nonlinear subdivision and multiscale transforms . Constructive Appoximation. submitted A family of subdivision schemes with cubic precision Pointwise smoothness,two-microlocalization and wavelets coefficients Using the refinement equations for the construction of pre-wavelets ii: Powers of two, Curves and Surfaces, pp.1-18155, 1991.
, A non-stationnary subdivsion scheme for curve interpolation Convexity preserving interpolatory subdivision scheme Monocity preserving interpolatory subdivision scheme Shape preserving interpolatory subdivision scheme for nonuniform data A variational approach to subdivision Using the discrete fourier-transform to analyze the convergence of subdivision schemes Convexity Preserving Interpolation. Stationary Nonlinear Subdivision and Splines Using laurent polynomial representation for the analysis of non-uniform binary subdivision scheme [Mal89] S. Mallat. A theory for multiresolution signal decomposition : the wavelet representation Local piecewise hyperbolic reconstruction of numerical fluxes for nonlinear scalar conservation laws, Lev00] A. Levin. Combined Subdivision schemesMal00] S. Mallat. A Wavelet Tour of Signal Processing. Academic PresMar94] A. MarquinaMat02] B. Matei. Méthodes Multirésolutions non-linéaires. Applications aux traitements d'imagesMat05] B. Matei. Smoothness characterization and stability in nonlinear multiscale framework: theoretical results. Asymptotic AnalysisMDL05] M. Marinov, N. Dyn, and D. Levin. Geometrically controlled 4-point interpolatory schemes. In A. Le Mehaute P.J. Laurent and L.L. Schumaker eds., editors, Advances in multiresolution for geometric modelling, pp.216-235609, 1989.
, A subdivision scheme for surfaces of revolution Computer Aided Geometrice Design Ondelettes et opérateurs I Subdivision scheme and irregular grids. Numerical Algorithms Efficient implementation of essentially non-oscillatory shockcapturing schemes i Efficient implementation of essentially non-oscillatory shockcapturing schemes ii Smoothness of nonlinear subdivision schemes Smoothness of nonlinear median-interpolation subdivision, Curves and Surfaces Fitting Modern Methods in Mathematics, pp.483-5021, 1988.
, Simple Regularity Criteria for Subdivision Schemes, SIAM Journal on Mathematical Analysis, vol.23, issue.6, pp.1544-1576251, 1992.
DOI : 10.1137/0523086
, Binary subdivision schemes for functions over irregular knot sequences Smothnness analysis of nonlinear subdivision schemes of homogenous and affine invariant type, Mathematical Method in CAGD III. 1995. [XY05], pp.511-546219, 1997.