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On Kolmogorov's Superposition Theorem and its Applications
A Nonlinear Model for Numerical Function Reconstruction from Discrete Data Sets in Higher Dimensions
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The book introduces a Regularization Network approach utilizing Kolmogorov's superposition theorem to reconstruct higher-dimensional continuous functions from discrete data points. It presents a new constructive proof of the theorem and explores its various versions, linking them to well-known approximation methods and Neural Networks. The work addresses the challenge of the curse of dimensionality, proposing a nonlinear model for function reconstruction within a reproducing kernel Hilbert space. It includes verification and analysis through numerous numerical examples.
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On Kolmogorov's Superposition Theorem and its Applications, Jürgen Braun
- Language
- Released
- 2010
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- (Paperback)
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- Title
- On Kolmogorov's Superposition Theorem and its Applications
- Subtitle
- A Nonlinear Model for Numerical Function Reconstruction from Discrete Data Sets in Higher Dimensions
- Language
- English
- Authors
- Jürgen Braun
- Released
- 2010
- Format
- Paperback
- Pages
- 192
- ISBN13
- 9783838116372
- Category
- Nature in general
- Description
- The book introduces a Regularization Network approach utilizing Kolmogorov's superposition theorem to reconstruct higher-dimensional continuous functions from discrete data points. It presents a new constructive proof of the theorem and explores its various versions, linking them to well-known approximation methods and Neural Networks. The work addresses the challenge of the curse of dimensionality, proposing a nonlinear model for function reconstruction within a reproducing kernel Hilbert space. It includes verification and analysis through numerous numerical examples.