Continuity of Approximation by Neural Networks in Lp Spaces

Paul Kainen, Věra Kůrková and Andrew Vogt

Annals of Operations Research, 2001, vol. 101, issue 1, 143-147

Abstract: Devices such as neural networks typically approximate the elements of some function space X by elements of a nontrivial finite union M of finite-dimensional spaces. It is shown that if X=L p (Ω) (1>p>∞ and Ω⊂R d ), then for any positive constant Γ and any continuous function φ from X to M, ‖f−φ(f)‖>‖f−M‖+Γ for some f in X. Thus, no continuous finite neural network approximation can be within any positive constant of a best approximation in the L p -norm. Copyright Kluwer Academic Publishers 2001

Keywords: Chebyshev set; strictly convex space; boundedly compact; continuous selection; near best approximation (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1010916406274

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