On Kolmogorov's Superposition Theorem and its Applications
A Nonlinear Model for Numerical Function Reconstruction from Discrete Data Sets in Higher Dimensions
Authors
Book rating
More about the book
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.
Book purchase
On Kolmogorov's Superposition Theorem and its Applications, Jürgen Braun
- Language
- Released
- 2010
- Binding
- (Paperback)
Payment methods
We’re missing your review here.
- 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
- Series
- Tags
- Non-Fiction, Textbooks, Science & Math, Nature, University Textbooks, Science, Mathematics, Mathematics and logic
- Rating
- 3 out of 5
- 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.