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1 results

  • 5 - Operator-Adapted Wavelets

  • from Part I - The Sobolev 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 63-89

  • Summary

    Wavelets adapted to a given self-adjoint elliptic operator are characterized by the requirement that they block-diagonalize the operator intouniformly well-conditioned and sparse blocks. These operator-adapted wavelets (gamblets) are constructed as orthogonalized hierarchies of nested optimal recovery splines obtained fromclassical/simple prewavelets(e.g., ~Haar) used as hierarchies of measurement functions. The resulting gamblet decomposition of an element in a Sobolev space is described andanalyzed.