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class="nav-link" href="/sparql/" title="Switch to /sparql endpoint"><i class="bi-box-arrow-up-right"></i> Sparql Endpoint </a> </li> </ul> </div> </div> </nav> <div style="margin-bottom: 60px"></div>   <section> <div class="container-xl"> <div class="row"> <div class="col"> <h1 id="title" class="display-6"><b>About:</b> <a href="http://dbpedia.org/resource/Incomplete_LU_factorization">Incomplete LU factorization</a> </h1> </div> </div> <div class="row"> <div class="col"> <div class="text-muted"> <span class="text-nowrap">An Entity of Type: <a href="javascript:void()">Thing</a>, </span> <span class="text-nowrap">from Named Graph: <a href="http://dbpedia.org">http://dbpedia.org</a>, </span> <span class="text-nowrap">within Data Space: <a href="http://dbpedia.org">dbpedia.org</a></span> </div> </div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> <p class="lead">In numerical linear algebra, an incomplete LU factorization (abbreviated as ILU) of a matrix is a sparse approximation of the LU factorization often used as a preconditioner.</p> </div> </div> </div> </section>   <section> <div class="container-xl"> <div class="row"> <div class="table-responsive"> <table class="table table-hover table-sm table-light"> <thead> <tr> <th class="col-xs-3 ">Property</th> <th class="col-xs-9 px-3">Value</th> </tr> </thead> <tbody> <tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/abstract"><small>dbo:</small>abstract</a> </td><td class="col-10 text-break"><ul> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="de" >Als ILU-Zerlegung (von incomplete LU-Decomposition) oder unvollst盲ndige LU-Zerlegung bezeichnet man in der numerischen Mathematik die fehlerbehaftete Zerlegung einer Matrix in das Produkt einer unteren Dreiecksmatrix L und einer oberen Dreiecksmatrix U , bei der von den Zerlegungsmatrizen L und U nur die Eintr盲ge einer vorgegebenen Besetzungsstruktur berechnet werden. Bei der Berechnung einer normalen LU-Zerlegung einer d眉nnbesetzten Matrix kann man die Besetzungsstruktur in der Regel nicht ausnutzen. Es wird daher sehr viel mehr Speicherplatz ben枚tigt als f眉r die urspr眉ngliche Matrix und auch die Anzahl der notwendigen Rechenoperationen ist nicht geringer als die f眉r eine vollbesetzte Matrix. Durch die Vorgabe einer maximalen Besetzungsstruktur wird dieses Problem unter Inkaufnahme einer fehlerbehafteten Zerlegung umgangen. Die ILU-Zerlegung wird erfolgreich als Vorkonditionierer zur Beschleunigung der iterativen L枚sung gro脽er d眉nnbesetzter linearer Gleichungssysteme mittels Krylow-Unterraum-Verfahren eingesetzt. Es werden dabei keine Eigenschaften des eigentlichen Problems (meist die numerische L枚sung einer partiellen Differentialgleichung) ausgenutzt. Damit ist sie nicht auf bestimmte Problemklassen beschr盲nkt und hat Einzug in viele Bereiche der numerischen Simulation gefunden, beispielsweise in der numerischen Str枚mungsmechanik ist die Technik weit verbreitet. Zuerst erw盲hnt wurde das Verfahren 1960 von Richard S. Varga und (N. I. Buleev). Eine genauere Analyse wurde 1977 von J. A. Meijerink und van der Vorst ver枚ffentlicht. Diese untersuchten Vorkonditionierungstechniken f眉r das CG-Verfahren und schlugen eine unvollst盲ndige Cholesky-Zerlegung f眉r symmetrische Matrizen vor. Gleichzeitig erw盲hnten sie eine Erweiterung auf allgemeine Matrizen.</span><small> (de)</small></span></li> <li><span class="literal"><span property="dbo:abstract" lang="en" >In numerical linear algebra, an incomplete LU factorization (abbreviated as ILU) of a matrix is a sparse approximation of the LU factorization often used as a preconditioner.</span><small> (en)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageExternalLink"><small>dbo:</small>wikiPageExternalLink</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="http://www.cfd-online.com/Wiki/Incomplete_LU_factorization_-_ILU" href="http://www.cfd-online.com/Wiki/Incomplete_LU_factorization_-_ILU">http://www.cfd-online.com/Wiki/Incomplete_LU_factorization_-_ILU</a></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" 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href="http://www.w3.org/2000/01/rdf-schema#comment"><small>rdfs:</small>comment</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="rdfs:comment" lang="en" >In numerical linear algebra, an incomplete LU factorization (abbreviated as ILU) of a matrix is a sparse approximation of the LU factorization often used as a preconditioner.</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="de" >Als ILU-Zerlegung (von incomplete LU-Decomposition) oder unvollst盲ndige LU-Zerlegung bezeichnet man in der numerischen Mathematik die fehlerbehaftete Zerlegung einer Matrix in das Produkt einer unteren Dreiecksmatrix L und einer oberen Dreiecksmatrix U , bei der von den Zerlegungsmatrizen L und U nur die Eintr盲ge einer vorgegebenen Besetzungsstruktur berechnet werden.</span><small> (de)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" 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