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标题：Effective Bounds on Strong Unicity in L1-Approximation
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作者：Ulrich Kohlenbach ; Paulo B. Oliva
期刊名称：BRICS Report Series
印刷版ISSN：0909-0878
出版年度：2001
卷号：8
期号：14
出版社：Aarhus University
摘要：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 [17]) to analyze Cheney's simplification [6] of Jackson's original proof [9] from 1921 of the uniqueness of the best L1-approximation of continuous functions f in C[0, 1] by polynomials p in Pn of degree generalizes `strong uniqueness' studied extensively in approximation theory). Moreover, the extracted modulus has the optimal epsilon-dependence as follows from Kroo [20]. The paper also describes how the uniform modulus of uniqueness can be used to compute the best L1-approximations of a fixed f in C[0, 1] with arbitrary precision, and includes some remarks on the case of best Chebychev approximation.