About: ON A SPARSE REPRESENTATION OF LAPLACIAN

Facets (new session)
Description
Metadata
Settings
- owl:sameAs
- Inference Rule:

About: ON A SPARSE REPRESENTATION OF LAPLACIAN Goto Sponge NotDistinct Permalink

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://acc-ern.tul.cz/images/journal/sbornik/ACC_Journal_4_2012.pdf
Description	One of the most important part of adaptive wavelet methods is an efficient approximate multiplication of stiffness matrices with vectors in wavelet coordinates. Although there are known algorithms to perform it in linear complexity, the application of them is relatively time consuming and its implementation is very difficult. Therefore, it is necessary to develop a wellconditioned wavelet basis with respect to which both the mass and stiffness matrices are sparse in the sense that the number of nonzero elements in any column is bounded by a constant. Then, matrix-vector multiplication can be performed exactly with linear complexity. We present here a wavelet basis on the interval with respect to which both the mass and stiffness matrices corresponding to the one-dimensional Laplacian are sparse. Consequently, the stiffness matrix corresponding to the n-dimensional Laplacian in tensor product wavelet basis is also sparse. Moreover, the constructed basis has an excellent condition number. In this contribution, we shortly review this construction and show several numerical tests. One of the most important part of adaptive wavelet methods is an efficient approximate multiplication of stiffness matrices with vectors in wavelet coordinates. Although there are known algorithms to perform it in linear complexity, the application of them is relatively time consuming and its implementation is very difficult. Therefore, it is necessary to develop a wellconditioned wavelet basis with respect to which both the mass and stiffness matrices are sparse in the sense that the number of nonzero elements in any column is bounded by a constant. Then, matrix-vector multiplication can be performed exactly with linear complexity. We present here a wavelet basis on the interval with respect to which both the mass and stiffness matrices corresponding to the one-dimensional Laplacian are sparse. Consequently, the stiffness matrix corresponding to the n-dimensional Laplacian in tensor product wavelet basis is also sparse. Moreover, the constructed basis has an excellent condition number. In this contribution, we shortly review this construction and show several numerical tests. (en)
Title	ON A SPARSE REPRESENTATION OF LAPLACIAN ON A SPARSE REPRESENTATION OF LAPLACIAN (en)
skos:prefLabel	ON A SPARSE REPRESENTATION OF LAPLACIAN ON A SPARSE REPRESENTATION OF LAPLACIAN (en)
skos:notation	RIV/46747885:24510/12:#0000805!RIV13-MSM-24510___
http://linked.open...avai/riv/aktivita	S
http://linked.open...avai/riv/aktivity	S
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Černá, Dana Finěk, Václav Ondračková, Zdeňka
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
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	156167
http://linked.open...ai/riv/idVysledku	RIV/46747885:24510/12:#0000805
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Wavelet; Hermite cubic splines; sparse representations. (en)
http://linked.open.../riv/klicoveSlovo	Wavelet Hermite cubic splines sparse representations.
http://linked.open...odStatuVydavatele	CZ - Česká republika
http://linked.open...ontrolniKodProRIV	[D79CB0BB9720]
http://linked.open...i/riv/nazevZdroje	ACC Journal
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	3 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	XVIII
http://linked.open...iv/tvurceVysledku	Finěk, Václav Černá, Dana Ondračková, Zdeňka
issn	1803-9782
number of pages	6 (xsd:int)
http://localhost/t...ganizacniJednotka	24510

Faceted Search & Find service v1.16.118 as of Jun 21 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Jun 21 2024, on Linux (x86_64-pc-linux-gnu), Single-Server Edition (126 GB total memory, 48 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software