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1 results

  • 16 - Fast Gamblet Transform

  • from Part III - The Banach Space Setting
  • Houman Owhadi, California Institute of Technology, Clint Scovel, California Institute of Technology
  • Book:
    Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
    Published online:
    10 October 2019
    Print publication:
    24 October 2019, pp 297-344

  • Summary

    The computation ofgamblets is accelerated by localizing their computation in a hierarchical manner (using a hierarchy of distances), and the approximation errors caused by these localization steps are bounded based on three properties: nesting, the well-conditioned nature of the linear systems solved in the Gamblet Transform, and theexponential decay of the gamblets. These efficiently computed, accurate, andlocalized gamblets are shown to producea Fast Gamblet Transform of near-linear complexity. Application to the three primary classes ofmeasurement functions in Sobolev spaces are developed.