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
9 - Gamblets
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
The minmax solution of the mixed extension of an optimal recovery game is evaluated in terms of the optimal recovery splines. Furthermore, the latter are given the interpretation of optimal bets in a mixed extension of the game corresponding to elementary components of the values of the measurement functions, giving rise to the interpretation of these optimal recovery splines as elementary bets, or gamblets. The screening effect is described and a rigorous proof of it established using exponential decay properties of the gamblets generated by Dirac delta measurement functions.
Keywords
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- Operator-Adapted Wavelets, Fast Solvers, and Numerical HomogenizationFrom a Game Theoretic Approach to Numerical Approximation and Algorithm Design, pp. 131 - 136Publisher: Cambridge University PressPrint publication year: 2019