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Einführendes Beispiel

In: Hierarchische Matrizen

Author

Listed:
  • Wolfgang Hackbusch

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

Abstract

Dass es blockweise möglich ist, eine Matrix zu vereinfachen, ist nicht neu. Paneel-Clusterungsmethoden (vgl. [90], [125, §7]), Multipolverfahren (vgl. [122], [125, §7.1.3.2]), Mosaikapproximation (vgl. [131]) und Matrixkompressionstechniken bei Wavelets (vgl. [35]) beruhen auf dem gleichen Konzept. Allerdings ist es in keinem dieser Fälle möglich, andere Matrixoperationen als die Matrixvektormultiplikation effizient durchzuführen. Deshalb soll in diesem Kapitel herausgestellt werden, wie die Matrixoperationen ausgeführt werden und was ihr Aufwand ist. Insbesondere wird sich herausstellen, dass alle Matrixoperationen mit fast linearem Aufwand berechnet werden können (statt $\mathcal{O}(n^2)$ oder $\mathcal{O}(n^3)$ wie bei voller Matrixdarstellung), wobei aber zu berücksichtigen ist, dass die Resultate im Allgemeinen Approximationsfehler enthalten.

Suggested Citation

  • Wolfgang Hackbusch, 2009. "Einführendes Beispiel," Springer Books, in: Hierarchische Matrizen, chapter 3, pages 43-54, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-00222-9_3
    DOI: 10.1007/978-3-642-00222-9_3
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