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Paulo Oliva (2002). On the Computational Complexity of Best L1-Approximation.

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    Proof Mining in L1-Approximation.Ulrich Kohlenbach & Paulo Oliva - 2003 - Annals of Pure and Applied Logic 121 (1):1-38.
    In this paper, we present another case study in the general project of proof mining which means the logical analysis of prima facie non-effective proofs with the aim of extracting new computationally relevant data. We use techniques based on monotone functional interpretation developed in Kohlenbach , Oxford University Press, Oxford, 1996, pp. 225–260) to analyze Cheney's simplification 189) of Jackson's original proof 320) of the uniqueness of the best L1-approximation of continuous functions fC[0,1] by polynomials pPn of degree n. Cheney's (...)
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