Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization 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
8 - Optimal Recovery Games on Hs0(Ω)
from Part II - The Game Theoretic Approach
Published online by Cambridge University Press: 10 October 2019
- 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
This chapter introduces two-person zero-sum games, optimal recovery games, and their lifts tomixed extended games and defines saddle points and minmax solutions.The optimal mixed strategy for the mixed extension of the optimal recovery games is generated by conditioning the canonical Gaussian field associated with the energy norm. Since the dependence ofthese optimal solutions on the measurement functions is through the conditioning process only, the canonical Gaussian field is referred to as a universal field. This fact demonstrates that the optimal solutions generated from a nested hierarchy of measurement functions form a martingale.
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- Operator-Adapted Wavelets, Fast Solvers, and Numerical HomogenizationFrom a Game Theoretic Approach to Numerical Approximation and Algorithm Design, pp. 119 - 130Publisher: Cambridge University PressPrint publication year: 2019