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| Titel |
Representation of planar integral-transformations by 4-D wavelet decomposition |
| VerfasserIn |
Wolfgang Keller, Jitka Hájková |
| Konferenz |
EGU General Assembly 2011
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 13 (2011) |
| Datensatznummer |
250047004
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| Zusammenfassung |
| In one way or the other numerical methods for the evaluation of integral operators can
often be related to the solution of the so-called Galerkin equations. For convolution
operators and exponentials with purely imaginary exponents as base function the
Galerkin matrix becomes diagonal and this fact is the core of the FFT techniques,
used in Physical Geodesy. For non-convolution operators the FFT technique is not
applicable.
This paper aims at the development of a technique, which also can be applied for
non-convolution operators. This technique is based on the use of wavelets as base
functions. In this case the Galerkin matrix is not diagonal but (after thresholding)
very sparse and this leads to methods, which are similarly efficient as FFT in the
convolution case. The paper starts with the theoretical background for n-dimensional
wavelet analysis and the representation of integral operators with respect to those
wavelet bases. The resulting algorithm is tested for convolution and non-convolution
operators. |
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