Abstract
We present a practical modification of the recent divide-and-conquer algorithms of [3] for approximating the eigenvalues of a real symmetric tridiagonal matrix. In this modified version, we avoid the numerical stability problems of the algorithms of [3] but preserve their insensitivity to clustering the eigenvalues and the possibility to give a priori upper bounds on their computational cost for any input matrix. We confirm the theoretical effectiveness of our algorithms by numerical experiments.
Zusammenfassung
Wir schlagen eine Modifikation der derzeitigen Divide-and-Conquer-Algorithmen aus [3] zur näherungsweisen Berechnung der Eigenwerte einer reelen symmetrischen Matrix vor. Dabei vermeiden wir die numerischen Stabilitätsprobleme dieser Algorithmen, erhalten aber ihre Unempfindlichkeit gegen das Auftreten von Eigenwerthaufen; wir können auch für unsere Modifikation a-priori Schranken für den Berechnungsaufwand für beliebige Matrizen angeben. Die theoretische Effizienz unseres Algorithmus bestätigen wir durch numerische Experimente.
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Dedicated to Professor Willard L. Miranker on the occasion of his 60th birthday
Supported by NSF Grants CCR-8805782 and CCR-9020690 and by 40% and 60% funds of MURST.
Supported by NSF Grants CCR-8805782 and CCR 9020690 and PSC-CUNY Award 661340.
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Bini, D., Pan, V. Practical improvement of the divide-and-conquer eigenvalue algorithms. Computing 48, 109–123 (1992). https://doi.org/10.1007/BF02241709
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DOI: https://doi.org/10.1007/BF02241709