Abstract
We present convergence and comparison theorems on parallel iterative multisplitting methods with different weighting schemes. In particular, we show that certain Gauss-Seidel multisplittings cannot converge faster than the usual Gauss-Seidel method. We also give numerical results on a 64 processor local memory computer. These experiments show that the ‘naive’ use of multisplittings can easily produce unsatisfactory results on parallel computers with more than just a few processors.
Zusammenfassung
Wir geben Konvergenz-und Vergleichsaussagen für parallele iterative Multisplitting-Verfahren mit verschiedenen Gewichtungsschemata. Insbesondere zeigen wir, daß bestimmte Gauss-Seidel Multisplitting-Verfahren nicht schneller konvergieren können als das gewöhnliche Gauss-Seidel-Verfahren. Wir berichten darüber hinaus über numerische Experimente auf einem 64-Prozessor-Rechner mit lokalem Speicher. Diese Experimente zeigen, daß der ‘naive’ Einsatz von Multisplittings leicht zu nicht zufriedenstellenden Ergebnissen führen kann, wenn mehr also nur ein paar Prozessoren eingesetzt werden.
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Frommer, A., Mayer, G. On the theory and practice of multisplitting methods in parallel computation. Computing 49, 63–74 (1992). https://doi.org/10.1007/BF02238650
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DOI: https://doi.org/10.1007/BF02238650