Houman Owhadi, Clint Scovel

Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization (eBook, PDF)

From a Game Theoretic Approach to Numerical Approximation and Algorithm Design

• Format: PDF

Produktbeschreibung

Presents interplays between numerical approximation and statistical inference as a pathway to simple solutions to fundamental problems.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 24. Oktober 2019
• Englisch
• ISBN-13: 9781108655644
• Artikelnr.: 70909402

Autorenporträt

Houman Owhadi is Professor of Applied and Computational Mathematics and Control and Dynamical Systems in the Computing and Mathematical Sciences department at the California Institute of Technology. He is one of the main editors of the Handbook of Uncertainty Quantification (2016). His research interests concern the exploration of interplays between numerical approximation, statistical inference and learning from a game theoretic perspective, especially the facilitation/automation possibilities emerging from these interplays.

Inhaltsangabe

1. Introduction
2. Sobolev space basics
3. Optimal recovery splines
4. Numerical homogenization
5. Operator adapted wavelets
6. Fast solvers
7. Gaussian fields
8. Optimal recovery games on $\mathcal{H}^{s}_{0}(\Omega)$
9. Gamblets
10. Hierarchical games
11. Banach space basics
12. Optimal recovery splines
13. Gamblets
14. Bounded condition numbers
15. Exponential decay
16. Fast Gamblet Transform
17. Gaussian measures, cylinder measures, and fields on $\mathcal{B}$
18. Recovery games on $\mathcal{B}$
19. Game theoretic interpretation of Gamblets
20. Survey of statistical numerical approximation
21. Positive definite matrices
22. Non-symmetric operators
23. Time dependent operators
24. Dense kernel matrices
25. Fundamental concepts.