| Autor: |
Steven B. Damelin, David L. Ragozin, Michael Werman |
| Rok vydání: |
2021 |
| Předmět: |
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| Zdroj: |
Applied and Numerical Harmonic Analysis ISBN: 9783030696368 |
| DOI: |
10.1007/978-3-030-69637-5_19 |
| Popis: |
We study min-max affine approximants of a continuous convex or concave function \(f:\Delta \subseteq \mathbb R^k\xrightarrow {} \mathbb R\), where Δ is a convex compact subset of \(\mathbb R^k\). In the case when Δ is a simplex, we prove that there is a vertical translate of the supporting hyperplane in \(\mathbb R^{k+1}\) of the graph of f at the vertices which is the unique best affine approximant to f on Δ. For k = 1, this result provides an extension of the Chebyshev equioscillation theorem for linear approximants. Our result has interesting connections to the computer graphics problem of rapid rendering of projective transformations. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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