Abstract
Several strategies for pivot selection in Givens reduction to upper triangular form and for row ordering within major steps of the reduction are compared on the grounds of how well they preserve sparsity. Recommendations are made based principally on the results of runs on test problems. The use of Givens similarity transformations in reducing a sparse matrix to Hessenberg form is similarly examined and finally some conclusions are drawn as to the advisability of using Givens reduction methods on sparse systems.
Zusammenfassung
Es werden verschiedene Strategien für die Pivotwahl der Givens Reduktion zu einer oberen Dreiecksform und für die Reihenfolge der Zeilen innerhalb größerer Hauptschritte der Reduktion verglichen, um zu erfahren, wie weit sie die Schwachbesetztheit bewahren. Die Empfehlungen stützen sich hauptsächlich auf die Ergebnisse von Testbeispielen. Zum Schluß wurde auch ein Vergleich mit der Householder Methode durchgeführt, und einige Schlußfolgerungen daraus gezogen.
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Duff, I.S. Pivot selection and row ordering in givens reduction on sparse matrices. Computing 13, 239–248 (1974). https://doi.org/10.1007/BF02241717
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DOI: https://doi.org/10.1007/BF02241717