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Kernel based Approximation Methods using MATLAB (Interdisciplinary Mathematical Sciences)

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Kernel based Approximation Methods using MATLAB (Interdisciplinary Mathematical Sciences) by Gregory E Fasshauer; Michael J Mccourt 9789814630153 9814630152

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Product details:

  • ISBN 10: 9814630152
  • ISBN 13: 9789814630153 
  • Author: Gregory E Fasshauer; Michael J Mccourt
In an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates their implementation in various settings. The authors explore the historical context of this fascinating topic and explain recent advances as strategies to address long-standing problems. Examples are drawn from fields as diverse as function approximation, spatial statistics, boundary value problems, machine learning, surrogate modeling and finance. Researchers from those and other fields can recreate the results within using the documented MATLAB code, also available through the online library. This combination of a strong theoretical foundation and accessible experimentation empowers readers to use positive definite kernels on their own problems of interest.

Table contents:

Part 1. Introduction

Part 2. Positive Definite Kernels and Reproducing Kernel Hilbert Spaces

Part 3. Examples of Kernels

Part 4. Kernels in MATLAB

Part 5. The Connection to Kriging

Part 6. The Connection to Green’s Kernels

Part 7. Iterated Brownian Bridge Kernels: A Green’s Kernel Example

Part 8. Generalized Sobolev Spaces

Part 9. Accuracy and Optimality of Reproducing Kernel Hilbert Space Methods

Part 10. “Flat” Limits

Part 11. The Uncertainty Principle – An Unfortunate Misconception

Part 12. Alternate Bases

Part 13. Stable Computation via the Hilbert–Schmidt SVD

Part 14. Parameter Optimization

Part 15. Scattered Data Fitting

Part 16. Computer Experiments and Surrogate Modeling

Part 17. Statistical Data Fitting via Gaussian Processes

Part 18. Machine Learning

Part 19. Derivatives of Interpolants and Hermite Interpolation

Part 20. Kernel-Based Methods for PDEs

Part 21. Finance

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