Analysis of a class of non linear subdivision schemes and associated multi-resolution transforms

2008/10/07 by Amat, S., Dadourian, K., Liandrat, J.
#41A05 #41A10 #65D05 #65D17 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.0810.1146

Abstract

This paper is devoted to the convergence and stability analysis of a class of nonlinear subdivision schemes and associated multi-resolution transforms. These schemes are defined as a perturbation of a linear subdivision scheme. Assuming a contractivity property, stability and convergence are derived. These results are then applied to various schemes such as uncentered interpolatory linear scheme, WENO scheme [13], Power-P scheme [16] and a non linear scheme using local spherical coordinates [18].

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