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Improving Jacobi and Gauss-Seidel iterations. (English) Zbl 0628.65022

Transformiert man das System \(x=Bx+b\) mit nichtnegativer Matrix B und \(b_{ii}=0\) durch einen Gauß-Eliminationsschritt in ein System der Form \(x=B'x+b\), so wird \(\rho\) (B’)\(\leq \rho (B)\) verbessert zu \(\rho (B')<\rho (B)\) für irreduzible Matrizen B. Für das transformierte System besitzt also das Gesamtschrittverfahren eine günstigere asymptotische Konvergenzrate als das alte. Unter einer Zusatzvoraussetzung wird dies auch für das Einzelschrittverfahren bewiesen.
Reviewer: O.Hübner

MSC:

65F10 Iterative numerical methods for linear systems

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References:

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