Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Multiresolution representation of data: a general framework
SIAM Journal on Numerical Analysis
Nonlinear pyramid transforms based on median-interpolation
SIAM Journal on Mathematical Analysis
Non-linear subdivision using local spherical coordinates
Computer Aided Geometric Design
Power ENO methods: a fifth-order accurate weighted power ENO method
Journal of Computational Physics
Analysis of a New Nonlinear Subdivision Scheme. Applications in Image Processing
Foundations of Computational Mathematics
On a class of L1-stable nonlinear cell-average multiresolution schemes
Journal of Computational and Applied Mathematics
A family of stable nonlinear nonseparable multiresolution schemes in 2D
Journal of Computational and Applied Mathematics
Weighted-powerp nonlinear subdivision schemes
Proceedings of the 7th international conference on Curves and Surfaces
A class of nonlinear four-point subdivision schemes
Advances in Computational Mathematics
High order nonlinear interpolatory reconstruction operators and associated multiresolution schemes
Journal of Computational and Applied Mathematics
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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).