Houman Owhadi

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

From a Game Theoretic Approach to Numerical Approximation and Algorithm Design

• Format: ePub

Produktbeschreibung

Although numerical approximation and statistical inference are traditionally covered as entirely separate subjects, they are intimately connected through the common purpose of making estimations with partial information. This book explores these connections from a game and decision theoretic perspective, showing how they constitute a pathway to developing simple and general methods for solving fundamental problems in both areas. It illustrates these interplays by addressing problems related to numerical homogenization, operator adapted wavelets, fast solvers, and Gaussian processes. This perspective reveals much of their essential anatomy and greatly facilitates advances in these areas, thereby appearing to establish a general principle for guiding the process of scientific discovery. This book is designed for graduate students, researchers, and engineers in mathematics, applied mathematics, and computer science, and particularly researchers interested in drawing on and developing this interface between approximation, inference, and learning.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 24. Oktober 2019
• Englisch
• ISBN-13: 9781108588041
• Artikelnr.: 62735807

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.