Advances in Computational Mathematics

, Volume 34, Issue 3, pp 253–277 | Cite as

Analysis of a class of nonlinear subdivision schemes and associated multiresolution transforms

  • S. Amat
  • K. Dadourian
  • J. LiandratEmail author


This paper is devoted to the convergence and stability analysis of a class of nonlinear subdivision schemes and associated multiresolution transforms. As soon as a nonlinear scheme can be written as a specific perturbation of a linear and convergent subdivision scheme, we show that if some contractivity properties are satisfied, then stability and convergence can be achieved. This approach is applied to various schemes, which give different new results. More precisely, we study uncentered Lagrange interpolatory linear schemes, WENO scheme (Liu et al., J Comput Phys 115:200–212, 1994), PPH and Power-P schemes (Amat and Liandrat, Appl Comput Harmon Anal 18(2):198–206, 2005; Serna and Marquina, J Comput Phys 194:632–658, 2004) and a nonlinear scheme using local spherical coordinates (Aspert et al., Comput Aided Geom Des 20:165–187, 2003). Finally, a stability proof is given for the multiresolution transform associated to a nonlinear scheme of Marinov et al. (2005).


Nonlinear subdivision schemes Nonlinear multiresolution Approximation Stability Convergence 

Mathematics Subject Classifications (2010)

41A05 41A10 65D05 65D17 


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Copyright information

© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

  1. 1.Departamento de Matemática Aplicada y EstadísticaUniversidad Politécnica de Cartagenade CartagenaSpain
  2. 2.Ecole Centrale Marseille, laboratoire d’analyse topologie et probabilites (LATP)Marseille cedex 20France

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