Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization From a Game Theoretic Approach to Numerical Approximation and Algorithm Design
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Reading Guide
- 1 Introduction
- Part I The Sobolev Space Setting
- Part II The Game Theoretic Approach
- 7 Gaussian Fields
- 8 Optimal Recovery Games on Hs0(Ω)
- 9 Gamblets
- 10 Hierarchical Games
- Part III The Banach Space Setting
- Part IV Game Theoretic Approach on Banach Spaces
- Part V Applications, Developments, and Open Problems
- Part VI Appendix
- Bibliography
- Algorithms
- Glossary
- Nomenclature
- Index
- Identities
10 - Hierarchical Games
from Part II - The Game Theoretic Approach
Published online by Cambridge University Press: 10 October 2019
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Reading Guide
- 1 Introduction
- Part I The Sobolev Space Setting
- Part II The Game Theoretic Approach
- 7 Gaussian Fields
- 8 Optimal Recovery Games on Hs0(Ω)
- 9 Gamblets
- 10 Hierarchical Games
- Part III The Banach Space Setting
- Part IV Game Theoretic Approach on Banach Spaces
- Part V Applications, Developments, and Open Problems
- Part VI Appendix
- Bibliography
- Algorithms
- Glossary
- Nomenclature
- Index
- Identities
Summary
Hierarchical optimalrecovery games are defined using a hierarchy of measurement functions. The sequence of optimal mixed minmax solutions is shown to be a martingale. Sparse rank-revealing representations of Gaussian fields are established.
Keywords
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- Operator-Adapted Wavelets, Fast Solvers, and Numerical HomogenizationFrom a Game Theoretic Approach to Numerical Approximation and Algorithm Design, pp. 137 - 148Publisher: Cambridge University PressPrint publication year: 2019