Are the degrees of best (co)convex and unconstrained polynomial approximation the same?

Kopotun, Kirill A.; Leviatan, D.; Shevchuk, I. A.

doi:10.1007/s10474-009-8111-4

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Overview Of Comonotone Approximation1

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2021

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Cited by 5 publications

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“…This overview deals only with comonotone approximation, q = 1; the complete picture is known also for q = 2, see [4,5] and Corollary 3, while for larger q the full generality has not been achieved. For a survey of shape-preserving, in particular q-coconvex, approximation see [3].…”

Section: Overview Of Comonotone Approximationmentioning

confidence: 99%

On the degree of piecewise shape-preserving approximation by polynomials

Vlasiuk¹

2015

Journal of Approximation Theory

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We show that the degree of piecewise q-coconvex approximation E (q) n ( f, Y s ) of a q-convex function by algebraic polynomials of degree < n asymptotically depends only on α, Y s and q,assuming this inequality holds for an N * dependent on f and that the degree of unconstrained approximation has the same decrease rate: n α E n ( f ) ≤ 1, n ≥ N with N ≤ s + q + 1. In particular, cases α > 1, N = s + 2, q = 1, and α > 2, N = s + 3, q = 2 complement earlier results on comonotone and coconvex approximation by polynomials respectively.

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Section: Overview Of Comonotone Approximationmentioning

confidence: 99%