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Formatierte Matrixoperationen für hierarchische Matrizen

In: Hierarchische Matrizen

Author

Listed:
  • Wolfgang Hackbusch

    (Max-Planck-Institut für Mathematik in den Naturwissenschaften Abteilung Wissenschaftliches Rechnen)

Abstract

Der wesentliche Fortschritt, der durch das Hilfsmittel der hierarchischen Matrizen erzielt wird, beruht auf der Möglichkeit, alle Matrixoperationen mit fast linearer Komplexität durchführen zu können. Deshalb spielt dieses Kapitel eine wichtige Rolle für die Implementierung. Da (abgesehen von der Matrix-Vektor-Multiplikation) die Resultate in Form einer $\mathcal{H}$ -Matrix ausgegeben werden, sprechen wir von einer formatierten Operation. Diese werden in §§7.1-7.6 algorithmisch vorgestellt. Die Analyse des hierfür benötigten Rechenaufwandes findet sich in §7.8. Im Falle der Addition und Multiplikation gibt es auch die Option einer exakten Berechnung, da das exakte Resultat für geeignete Parameter eine $\mathcal{H}$ -Matrix darstellt (vgl. Korollar 7.3.2 und Lemma 7.4.5). Zu parallelen Implementierungen, die hier nicht diskutiert werden, findet man Details in Kriemann [103, 102, 104] und Bebendorf-Kriemann [14].

Suggested Citation

  • Wolfgang Hackbusch, 2009. "Formatierte Matrixoperationen für hierarchische Matrizen," Springer Books, in: Hierarchische Matrizen, chapter 7, pages 147-190, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-00222-9_7
    DOI: 10.1007/978-3-642-00222-9_7
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