Mathematical Research Letters

Volume 7 (2000)

Number 3

The shape of the error in wavelet approximation and piecewise linear interpolation

Pages: 317 – 327

DOI: http://dx.doi.org/10.4310/MRL.2000.v7.n3.a6

Author

Robert S. Strichartz (Cornell University)

Abstract

The graph of the error in wavelet approximation, when properly rescaled, is shown to converge in the Hausdorff metric to a limit set $\Gamma$. The limit set $\Gamma$ is not a graph of a function, but rather a region bounded by the graphs of multiples of a derivative of the function, depending on the first nonvanishing moment of the wavelet. A similar result is shown for piecewise linear interpolation. Higher dimensional analogs are discussed.

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