Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization

Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization

From a Game Theoretic Approach to Numerical Approximation and Algorithm Design

Scovel, Clint (California Institute of Technology); Owhadi, Houman (California Institute of Technology)

Cambridge University Press

10/2019

488

Dura

Inglês

9781108484367

Pré-lançamento - envio 15 a 20 dias após a sua edição

This book, meant for graduate students and researchers, explores the connections between numerical approximation and statistical inference from a game and decision theoretic perspective, and illustrates these interplays by addressing problems related to numerical homogenization, operator adapted wavelets, and fast solvers.
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.
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