Abstract
A fast verification algorithm of calculating guaranteed error bounds for all approximate eigenvalues of a real symmetric matrix is proposed. In the proposed algorithm, Rump’s and Wilkinson’s bounds are combined. By introducing Wilkinson’s bound, it is possible to improve the error bound obtained by the verification algorithm based on Rump’s bound with a small additional cost. Finally, this paper includes some numerical examples to show the efficiency of the proposed algorithm.
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© 2005 Springer-Verlag Berlin Heidelberg
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Miyajima, S., Ogita, T., Oishi, S. (2005). Fast Verification for Respective Eigenvalues of Symmetric Matrix. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2005. Lecture Notes in Computer Science, vol 3718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11555964_26
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DOI: https://doi.org/10.1007/11555964_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28966-1
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