Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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TWO-SIDED BEST SIMULTANEOUS APPROXIMATION

  • Received : 2010.07.21
  • Accepted : 2010.11.09
  • Published : 2010.12.30
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Abstract

Let $C_1(X)$ be a normed linear space over ${\mathbb{R}}^m$, and S be an n-dimensional subspace of $C_1(X)$ with spaned by {$s_1,{\cdots},s_n$}. For each ${\ell}$- tuple vectors F in $C_1(X)$, the two-sided best simultaneous approximation problem is $$\min_{s{\in}S}\;\max\limits_{i=1}^\ell\{{\parallel}f_i-s{\parallel}_1\}$$. A $s{\in}S$ attaining the above minimum is called a two-sided best simultaneous approximation or a Chebyshev center for $F=\{f_1,{\cdots},f_{\ell}\}$ from S. This paper is concerned with algorithm for calculating two-sided best simultaneous approximation, in the case of continuous functions.

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Acknowledgement

Supported by : Duksung Women's University

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