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Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization from Part I - The Sobolev Space Setting
Published online by Cambridge University Press: 10 October 2019
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.
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