Operator-adapted wavelets, fast solvers, and numerical homogenization : from a game theoretic approach to numerical approximation and algorithm design
著者
書誌事項
Operator-adapted wavelets, fast solvers, and numerical homogenization : from a game theoretic approach to numerical approximation and algorithm design
（Cambridge monographs on applied and computational mathematics）
Cambridge University Press, 2019
- タイトル別名
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Operator adapted wavelets, fast solvers, and numerical homogenization
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注記
Bibliography: p. 444-459
Includes index
内容説明・目次
内容説明
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.
目次
- 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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