NANAOct 7, 2008

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

arXiv:0810.11461.27 citationsh-index: 30
Originality Synthesis-oriented
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Provides theoretical guarantees for nonlinear subdivision schemes, benefiting researchers in geometric modeling and signal processing.

The paper analyzes convergence and stability of a class of nonlinear subdivision schemes defined as perturbations of linear schemes, deriving conditions under contractivity. Results are applied to several existing schemes.

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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