Representation of planar integral-transformations by 4-D wavelet decomposition

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F11%3A43896589" target="_blank" >RIV/49777513:23520/11:43896589 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1007/s00190-010-0440-0" target="_blank" >http://dx.doi.org/10.1007/s00190-010-0440-0</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00190-010-0440-0" target="_blank" >10.1007/s00190-010-0440-0</a>

Result language

angličtina

Original language name

Representation of planar integral-transformations by 4-D wavelet decomposition

Original language description

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 functions the Galerkin matrix becomesdiagonal 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 can also 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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

DE - Earth magnetism, geodesy, geography

OECD FORD branch

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Project

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Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2011

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

JOURNAL OF GEODESY

ISSN

0949-7714

e-ISSN

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Volume of the periodical

85

Issue of the periodical within the volume

6

Country of publishing house

DE - GERMANY

Number of pages

16

Pages from-to

341-356

UT code for WoS article

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EID of the result in the Scopus database

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