Stability of manifold-valued subdivision schemes and multiscale transformations (Q607487)
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scientific article; zbMATH DE number 5818054
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stability of manifold-valued subdivision schemes and multiscale transformations |
scientific article; zbMATH DE number 5818054 |
Statements
Stability of manifold-valued subdivision schemes and multiscale transformations (English)
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22 November 2010
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It is well known that along with a linear subdivision scheme a multiscale transformation is defined, such transformation can also be defined in nonlinear setting. Here the author introduces a new kind of proximity condition which bounds the difference of the differential of a nonlinear subdivision scheme and a linear one. It turns out that-unlike the generic nonlinear case and modulo some minor technical assumptions in the manifold-valued setting, convergence implies stability of the nonlinear subdivision scheme and associated nonlinear multiscale transformations.
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Lipschitz-interpolatory wavelet transform
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manifold-valued data
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nonlinear subdivision
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