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Approximate Interpolation by Neural Networks with the Inverse Multiquadric Functions

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Advances in Computation and Intelligence (ISICA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4683))

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Abstract

For approximate interpolation, a type of single-hidden layer feedforward neural networks with the inverse multiquadric activation function is presented in this paper. We give a new and quantitative proof of the fact that a single layer neural networks with n + 1 hidden neurons can learn n + 1 distinct samples with zero error. Based on this result, approximate interpolants are given. They can approximate interpolate, with arbitrary precision, any set of distinct data in one or several dimensions. They can uniformly approximate any C 1 continuous function of one variable.

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Authors and Affiliations

  1. School of Mathematical Sciences and Computing Technology, Central South University, 410083 Changsha, China

    Xuli Han

Authors
  1. Xuli Han
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Editor information

Lishan Kang Yong Liu Sanyou Zeng

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© 2007 Springer-Verlag Berlin Heidelberg

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Han, X. (2007). Approximate Interpolation by Neural Networks with the Inverse Multiquadric Functions. In: Kang, L., Liu, Y., Zeng, S. (eds) Advances in Computation and Intelligence. ISICA 2007. Lecture Notes in Computer Science, vol 4683. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74581-5_32

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  • DOI: https://doi.org/10.1007/978-3-540-74581-5_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74580-8

  • Online ISBN: 978-3-540-74581-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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