About: Matrix-Vector Multiplication in Adaptive Wavelet Methods

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://proceedings.aip.org/resource/2/apcpcs/1410/1/147_1?isAuthorized=no
Description	Wavelet based methods are an established tool in signal and image processing and a promising tool for the numerical solution of operator equations. They have namely some interesting properties which may provide an advantage over classical methods. It is well-known fact that representations of smooth functions and also representations of a wide class of operators are sparse in wavelet coordinates. Further advantage of wavelet methods consists in the existence of a diagonal preconditioner. The condition number of the preconditioned stiffness matrices does not depend on the size of matrices. Although the stiffness matrices in wavelet coordinates are only quasi sparse, an approximate multiplication of these matrices with given sparse vectors can be performed in the linear complexity. These are crucial parts to design efficient adaptive wavelet schemes. In this contribution, we focus on biorthogonal spline wavelets and we compare different approximate matrix-vector multiplication techniques. Wavelet based methods are an established tool in signal and image processing and a promising tool for the numerical solution of operator equations. They have namely some interesting properties which may provide an advantage over classical methods. It is well-known fact that representations of smooth functions and also representations of a wide class of operators are sparse in wavelet coordinates. Further advantage of wavelet methods consists in the existence of a diagonal preconditioner. The condition number of the preconditioned stiffness matrices does not depend on the size of matrices. Although the stiffness matrices in wavelet coordinates are only quasi sparse, an approximate multiplication of these matrices with given sparse vectors can be performed in the linear complexity. These are crucial parts to design efficient adaptive wavelet schemes. In this contribution, we focus on biorthogonal spline wavelets and we compare different approximate matrix-vector multiplication techniques. (en)
Title	Matrix-Vector Multiplication in Adaptive Wavelet Methods Matrix-Vector Multiplication in Adaptive Wavelet Methods (en)
skos:prefLabel	Matrix-Vector Multiplication in Adaptive Wavelet Methods Matrix-Vector Multiplication in Adaptive Wavelet Methods (en)
skos:notation	RIV/46747885:24510/11:#0000787!RIV13-GA0-24510___
http://linked.open...avai/predkladatel	Fakulta přírodovědně-humanitní a pedagogická
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GP201/09/P641)
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Černá, Dana Finěk, Václav
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Technická univerzita v Liberci / Fakulta přírodovědně-humanitní a pedagogická
http://linked.open...dnocenehoVysledku	210968
http://linked.open...ai/riv/idVysledku	RIV/46747885:24510/11:#0000787
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	matrix algebra; signal processing; mathematical operators; simulation; partial differential equations (en)
http://linked.open.../riv/klicoveSlovo	signal processing simulation matrix algebra partial differential equations mathematical operators
http://linked.open...ontrolniKodProRIV	[633F5AA7F06A]
http://linked.open...v/mistoKonaniAkce	Sozopol, Bulgaria
http://linked.open...i/riv/mistoVydani	Melville, New York
http://linked.open...i/riv/nazevZdroje	APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE '11)
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Wavelet adaptive methods with stable bases
http://linked.open...UplatneniVysledku	2011
http://linked.open...iv/tvurceVysledku	Finěk, Václav Černá, Dana
http://linked.open...vavai/riv/typAkce	EUR - Evropská
http://linked.open...ain/vavai/riv/wos	301975000015
http://linked.open.../riv/zahajeniAkce	2011-01-01 (xsd:date)
number of pages	395 (xsd:int)
http://bibframe.org/vocab/doi	10.1063/1.3664365
http://purl.org/ne...btex#hasPublisher	American Institute of Physics
https://schema.org/isbn	978-0-7354-0984-2
http://localhost/t...ganizacniJednotka	24510
is http://linked.open...avai/riv/vysledek of	Matrix-Vector Multiplication in Adaptive Wavelet Methods

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