\(\sqrt 3\)-subdivision schemes: Maximal sum rule orders (Q1404483)
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scientific article; zbMATH DE number 1969070
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(\sqrt 3\)-subdivision schemes: Maximal sum rule orders |
scientific article; zbMATH DE number 1969070 |
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\(\sqrt 3\)-subdivision schemes: Maximal sum rule orders (English)
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21 August 2003
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The paper deals with the problem of achieving maximal sum rule orders for stationary \(\sqrt 3\)-subdivision schemes with given mask support. Exact formulas for the maximal sum rule order are obtained by studying interpolating and approximating schemes for a natural family of symmetric mask support sets related to squares. Some properties of multivariate Lagrange polynomial interpolation are used to prove the existence of interpolating schemes with maximal sum rule orders. Several examples of smooth interpolating \(\sqrt 3\)-subdivision schemes are also constructed.
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surface subdivision
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sum rule order
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numerical examples
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multivariate Lagrange polynomial interpolation
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