Abstract
In this paper we present a systematic method which computes bounds for invariant subspaces belonging to a double or nearly double eigenvalue. Furthermore an algorithm based on interval arithmetic tools is introduced which improves these bounds systematically.
Zusammenfassung
In dieser Arbeit bringen wir eine systematische Methode zur Berechnung von Schranken für invariante Teilräume, die zu einem doppelten oder fast doppelten Eigenwert gehören. Außerdem wird ein auf intervallarithmetischen Hilfsmitteln aufgebauter Algorithmus angegeben, der diese Schranken systematisch verbessert.
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References
Alefeld, G., Herzberger, J.: Introduction to Interval Computations. Academic Press 1983.
Alefeld, G., Platzöder, L.: A quadratically convergent Krawczyk-like algorithm. SIAM J. Numer. Anal.,20, 210–219 (1983).
Dongarra, J. J., Moler, C. B., Wilkinson, J. H.: Improving the accuracy of computed eigenvalues and eigenvectors. SIAM J. Numer. Anal.20, 23–45 (1983).
Kulisch, U., Miranker, W. L.: A new approach to Scientific Computation. Notes and Reports in Computer Science and Applied Mathematics. Academic Press 1983.
Rump, S.: Solving algebraic problems with high accuracy. In [4] Kulisch, U., Miranker, W. L.: A new approach to Scientific Computation. Notes and Reports in Computer Science and Applied Mathematics. Academic Press 1983, 53–120.
Symm, H. J., Wilkinson, J. H.: Realistic error bounds for a simple eigenvalue and its associated eigenvector. Numer. Math.35, 113–126 (1980).
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Dedicated to Professor W. Knödel on the occasion of his 60th birthday
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Alefeld, G., Spreuer, H. Iterative improvement of componentwise errorbounds for invariant subspaces belonging to a double or nearly double eigenvalue. Computing 36, 321–334 (1986). https://doi.org/10.1007/BF02240207
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DOI: https://doi.org/10.1007/BF02240207