Abstract
The present paper gives a converse result by showing that there exists a functionf ∈C [−1,1], which satisfies that sgn(x)f(x) ≥ 0 forx ∈ [−1, 1], such that {fx75-1} whereE (0) n (f, 1) is the best approximation of degreen tof by polynomials which are copositive with it, that is, polynomialsP withP(x(f(x) ≥ 0 for allx ∈ [−1, 1],E n(f) is the ordinary best polynomial approximation off of degreen.
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Zhou, S.P. A counterexample in copositive approximation. Israel J. Math. 78, 75–83 (1992). https://doi.org/10.1007/BF02801572
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DOI: https://doi.org/10.1007/BF02801572