Abstract
Backward stability of Gauss-Jordan elimination is discussed. The method proposed in [4] with some modifications is used. The basic tool of this method is the graph of the algorithm and its parallel structure. The systemUx=c, whereU is ann×n upper triangular matrix, is considered for simplicity. Then estimates of the equivalent perturbations depending quadratically onn are obtained.
Zusammenfassung
Es wird die rückwärtige Stabilität der Gauß-Jordan Elimination betrachtet. Dabei wird die in [4] vorgeschlagene Methode mit einigen Veränderungen angewendet. Grundmittel dieser Methode ist der Graph des Algorithmus und seine parallele Struktur. Zur Vereinfachung wurde das lineare SystemUx=c betrachtet, wobeiU eine obere dreieckigen×n-Matrix ist. Darauf ergeben sich Schätzwerte der äquivalenten Störungen, die inn quadratisch sind.
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References
Dekker T. J., Hoffmann W.: Rehabilitation of the Gauss-Jordan algorithm. Numer. Math.,54, 591 (1989).
Peters G., Wilkinson J. H.: On the stability of Gauss-Jordan elimination with pivoting. Commun. ACM,18, 20 (1975).
Stummel F.: Perturbation theory for evaluation algorithms of arithmetic expressions. Math. Comp.,37, 435 (1981).
Voevodin V. V., Yalamov P. Y.: A new method of round-off error estimation. In: Boyanov K., Markov St., Eds., Proc. Workshop on Parallel and Distributed Processing, March 1990, Sofia (Elsevier, Amstedam) 315 (1990).
Wilkinson J. H.: The algebraic eigenvalue problem Oxford: Clarendon Press 1965.
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Yalamov, P.Y. On the backward stability of Gauss-Jordan elimination. Computing 47, 193–197 (1991). https://doi.org/10.1007/BF02253434
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DOI: https://doi.org/10.1007/BF02253434