On Min-Max Affine Approximants of Convex or Concave Real-Valued Functions from ℝk, Chebyshev Equioscillation and Graphics

Steven B. Damelin*, David L. Ragozin, Michael Werman

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

1 Scopus citations

Abstract

We study min-max affine approximants of a continuous convex or concave function f:Δ⊆ℝk→ℝ, where Δ is a convex compact subset of ℝk. In the case when Δ is a simplex, we prove that there is a vertical translate of the supporting hyperplane in ℝk+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.

Original languageAmerican English
Title of host publicationApplied and Numerical Harmonic Analysis
PublisherBirkhauser
Pages373-383
Number of pages11
StatePublished - 2021

Publication series

NameApplied and Numerical Harmonic Analysis
ISSN (Print)2296-5009
ISSN (Electronic)2296-5017

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

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