Presents interplays between numerical approximation and statistical inference as a pathway to simple solutions to fundamental problems.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
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.
