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 language||American English|
|Title of host publication||Applied and Numerical Harmonic Analysis|
|Number of pages||11|
|State||Published - 2021|
|Name||Applied and Numerical Harmonic Analysis|
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© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.