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
7 - Gaussian Fields
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 purpose of this chapter is to introduce the canonical Gaussian field defined bythe energy norm of the operator,which will play a central role in the interplay among the results of the previous chapters, Gaussian process regression, and game theory. The chapter begins witha presentation of basic definitions and results related to Gaussian random variables, Gaussian vectors, Gaussian spaces, Gaussian conditioning, Gaussian processes, Gaussian measures, and Gaussian fields.
Keywords
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- Information
- Operator-Adapted Wavelets, Fast Solvers, and Numerical HomogenizationFrom a Game Theoretic Approach to Numerical Approximation and Algorithm Design, pp. 105 - 118Publisher: Cambridge University PressPrint publication year: 2019