Approximate multiplication in adaptive wavelet methods

Kód výsledku v IS VaVaI

RIV/46747885:24510/12:#0001005 - isvavai.cz

Výsledek na webu

http://link.springer.com/article/10.2478%2Fs11533-013-0216-x

DOI - Digital Object Identifier

10.2478/s11533-013-0216-x

Jazyk výsledku

angličtina

Název v původním jazyce

Approximate multiplication in adaptive wavelet methods

Popis výsledku v původním jazyce

Cohen, Dahmen and DeVore designed in [Adaptive wavelet methods for elliptic operator equations: convergence rates, Math. Comp., 2001, 70(233), 27?75] and [Adaptive wavelet methods IIbeyond the elliptic case, Found. Comput. Math., 2002, 2(3), 203?245] a general concept for solving operator equations. Its essential steps are: transformation of the variational formulation into the well-conditioned infinite-dimensional l 2-problem, finding the convergent iteration process for the l 2-problem and finally using its finite dimensional approximation which works with an inexact right-hand side and approximate matrix-vector multiplication. In our contribution, we pay attention to approximate matrix-vector multiplication which is enabled by an off-diagonal decayof entries of the wavelet stiffness matrices. We propose a more efficient technique which better utilizes actual decay of matrix and vector entries and we also prove that this multiplication algorithm is asymptotically optimal in the sens

Název v anglickém jazyce

Approximate multiplication in adaptive wavelet methods

Popis výsledku anglicky

Cohen, Dahmen and DeVore designed in [Adaptive wavelet methods for elliptic operator equations: convergence rates, Math. Comp., 2001, 70(233), 27?75] and [Adaptive wavelet methods IIbeyond the elliptic case, Found. Comput. Math., 2002, 2(3), 203?245] a general concept for solving operator equations. Its essential steps are: transformation of the variational formulation into the well-conditioned infinite-dimensional l 2-problem, finding the convergent iteration process for the l 2-problem and finally using its finite dimensional approximation which works with an inexact right-hand side and approximate matrix-vector multiplication. In our contribution, we pay attention to approximate matrix-vector multiplication which is enabled by an off-diagonal decayof entries of the wavelet stiffness matrices. We propose a more efficient technique which better utilizes actual decay of matrix and vector entries and we also prove that this multiplication algorithm is asymptotically optimal in the sens

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

GP201/09/P641: Waveletové adaptivní metody se stabilními bázemi

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS

ISSN

1895-1074

e-ISSN

—

Svazek periodika

11

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

PL - Polská republika

Počet stran výsledku

12

Strana od-do

972-983

Kód UT WoS článku

316284500014

EID výsledku v databázi Scopus

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