Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization - Clint Scovel

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

Biographie:
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.

Sommaire:
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 dollars\mathcal{H}^{s}_{0}(\Omega) dollars; 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 dollars\mathcal{B} dollars; 18. Recovery games on dollars\mathcal{B} dollars; 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.