TY  - BOOK
AU  - Fasshauer,Gregory
AU  - McCourt,Michael
TI  - Kernel-based approximation methods using MATLAB
T2  - Interdisciplinary mathematical sciences
SN  - 9789814630139 (hardcover : alk. paper)
U1  - 511.42 23
PY  - 2016///
CY  - Singapore
PB  - World Scientific
KW  - Approximation theory
KW  - Mathematics
KW  - Kernel functions
N1  - Includes bibliographical references and index; 1. Introduction --
2. Positive definite Kernels and reproducing Kernel Hilbert spaces --
3. Examples of Kernels --
4. Kernels in MATLAB --
5. The connection to Kriging --
6. The connection to Green;s Kernels --
7. Iterated Brownian bridge Kernels: a green's Kernel example --
8. Generalized sobolev spaces --
9. Accuracy and optimality of reproducing Kernel Hilbert --
10. "Flat" limits --
11. The uncertainty principle - an unfortunate misconception --
12. Alternate bases --
13. Stable computation via the Hilbert-Schmidt SVD --
14. Parameter optimization --
15. Scattered data fitting --
16. Computer experiments and surrogate modeling --
17. Statistical data fitting via Gaussian processes --
18. Machine learning --
19. Derivatives of interpolants and Hermite interpolation --
20. Kernel-Based methods for PDEs --
21. Finance --
Appendices
N2  - 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
ER  -