Zusammenfassung
Viele praktische Probleme führen zu der Aufgabe, sehr große lineare Gleichungssyteme Ax = b zu lösen, bei denen glücklicherweise die Matrix A nur schwach besetzt ist, d. h. nur relativ wenige nicht verschwindende Komponenten besitzt. Solche Gleichungssysteme erhält man z. B. bei der Anwendung von Differenzenverfahren oder finite-element Methoden zur näherungsweisen Lösung von Randwertaufgaben bei partiellen Differentialgleichungen. Die üblichen Eliminationsverfahren [s. Kapitel 4] können hier nicht ohne weiteres zur Lösung verwandt werden, weil sie ohne besondere Maßnahmen gewöhnlich zur Bildung von mehr oder weniger voll besetzten Zwischenmatrizen führen und deshalb die Zahl der zur Lösung erforderlichen Rechenoperationen auch für die heutigen Rechner zu groß wird, abgesehen davon, daß die Zwischenmatrizen nicht mehr in die üblicherweise verfügbaren Maschinenspeicher passen.
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Stoer, J., Bulirsch, R. (2000). Iterationsverfahren zur Lösung großer linearer Gleichungssysteme, einige weitere Verfahren. In: Numerische Mathematik 2. Springer-Lehrbuch. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09025-1_3
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