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13 - Gamblets

from Part III - The Banach Space Setting

Published online by Cambridge University Press:  10 October 2019

Houman Owhadi
Affiliation:
California Institute of Technology
Clint Scovel
Affiliation:
California Institute of Technology
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Summary

This chapter generalizes and extends the development ofoperator-adapted wavelets (gamblets)and their resulting multiresolution decompositionsfrom Sobolev spaces to Banach spaces equipped with a quadraticnorm and a nonstandard dual pairing. The fundamental importance of the Schur complement is elucidated and the geometric nature of gamblets is presented from two views: one regarding basis transformations derived from the nesting, and the other the linear transformations associated with these basis transformations. A table of gamblet identities is presented.

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Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
From a Game Theoretic Approach to Numerical Approximation and Algorithm Design
, pp. 160 - 194
Publisher: Cambridge University Press
Print publication year: 2019

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  • Gamblets
  • Houman Owhadi, California Institute of Technology, Clint Scovel, California Institute of Technology
  • Book: Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
  • Online publication: 10 October 2019
  • Chapter DOI: https://doi.org/10.1017/9781108594967.018
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  • Gamblets
  • Houman Owhadi, California Institute of Technology, Clint Scovel, California Institute of Technology
  • Book: Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
  • Online publication: 10 October 2019
  • Chapter DOI: https://doi.org/10.1017/9781108594967.018
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Gamblets
  • Houman Owhadi, California Institute of Technology, Clint Scovel, California Institute of Technology
  • Book: Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
  • Online publication: 10 October 2019
  • Chapter DOI: https://doi.org/10.1017/9781108594967.018
Available formats
×