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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

DE - Zemský magnetismus, geodesie, geografie

OECD FORD obor

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Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2011

Kód důvěrnosti údajů

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

Název periodika

JOURNAL OF GEODESY

ISSN

0949-7714

e-ISSN

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Svazek periodika

85

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

16

Strana od-do

341-356

Kód UT WoS článku

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EID výsledku v databázi Scopus

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