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1 results

  • 14 - Bounded Condition Numbers

  • 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 195-251

  • Summary

    This chapter bounds the condition numbers of thestiffness matrix of operator-adapted wavelets within each subband (scale). These resulting bounds are characterized through weak alignment conditions between measurement functions and eigensubspaces of the underlying operator. In Sobolev spaces, these alignment conditions translate into approximate error estimates associated with variational splines andscattered data approximation. These estimates are established for the three primary examples, subsampled Diracs, Haar prewavelets, and local polynomials,of hierarchies of measurement functions in Sobolev spaces.