Proof mining in L1-approximation

Annals of Pure and Applied Logic 121 (1):1-38 (2003)
  Copy   BIBTEX

Abstract

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 proof is non-effective in the sense that it is based on classical logic and on the non-computational principle WKL . The result of our analysis provides the first effective uniform modulus of uniqueness . Moreover, the extracted modulus has the optimal ε-dependency as follows from Kroó 331). The paper also describes how the uniform modulus of uniqueness can be used to compute the best L1-approximations of a fixed fC[0,1] with arbitrary precision. The second author uses this result to give a complexity upper bound on the computation of the best L1-approximation in Oliva 66–77)

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 93,590

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Analytics

Added to PP
2014-01-16

Downloads
27 (#142,020)

6 months
15 (#941,355)

Historical graph of downloads
How can I increase my downloads?