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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Neural networks for localized approximation
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by C. K. Chui, Xin Li and H. N. Mhaskar PDF
Math. Comp. 63 (1994), 607-623 Request permission

Abstract:

We prove that feedforward artificial neural networks with a single hidden layer and an ideal sigmoidal response function cannot provide localized approximation in a Euclidean space of dimension higher than one. We also show that networks with two hidden layers can be designed to provide localized approximation. Since wavelet bases are most effective for local approximation, we give a discussion of the implementation of spline wavelets using multilayered networks where the response function is a sigmoidal function of order at least two.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Math. Comp. 63 (1994), 607-623
  • MSC: Primary 65D15; Secondary 41A15, 41A30, 92B20
  • DOI: https://doi.org/10.1090/S0025-5718-1994-1240656-2
  • MathSciNet review: 1240656