Hierarchische Matrizen

Wolfgang Hackbusch

Wolfgang Hackbusch
Hierarchische Matrizen [PDF ebook]
Algorithmen und Analysis

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Bei der Diskretisierung von Randwertaufgaben und Integralgleichungen entstehen große, eventuell auch voll besetzte Matrizen. In dem Band stellt der Autor eine neuartige Methode dar, die es erstmals erlaubt, solche Matrizen nicht nur effizient zu speichern, sondern auch alle Matrixoperationen einschließlich der Matrixinversion bzw. der Dreieckszerlegung approximativ durchzuführen. Anwendung findet diese Technik nicht nur bei der Lösung großer Gleichungssysteme, sondern auch bei Matrixgleichungen und der Berechnung von Matrixfunktionen.

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Table des matières

Rang–Matrizen.- Einf#x00FC;hrendes Beispiel.- Separable Entwicklung und ihr Bezug zu Niedrigrangmatrizen.- Matrixpartition.- Definition und Eigenschaften der hierarchischen Matrizen.- Formatierte Matrixoperationen f#x00FC;r hierarchische Matrizen.- -Matrizen.- Verschiedene Erg#x00E4;nzungen.- Anwendungen auf diskretisierte Integraloperatoren.- Anwendungen auf Finite-Element-Matrizen.- Inversion mit partieller Auswertung.- Matrixfunktionen.- Matrixgleichungen.- Tensorprodukte.

A propos de l’auteur

Arbeitsfeld des Autors:Diskretisierung partieller Differentialgleichungen, Diskretisierung von Integralgleichungen (Randelementmethoden), schnelle Lösung großer Gleichungssysteme, Mehrgittermethoden Auszeichnungen:Leibniz-Preis, Brouwer-Medaille

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Langue Allemand ● Format PDF ● Pages 451 ● ISBN 9783642002229 ● Taille du fichier 7.1 MB ● Maison d’édition Springer Berlin ● Lieu Heidelberg ● Pays DE ● Publié 2009 ● Téléchargeable 24 mois ● Devise EUR ● ID 2170140 ● Protection contre la copie Adobe DRM

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