Abstract
LExpRes is a k-step explicit restart variant of the Lanczos algorithm. In this method a periodic/selective reorthogonalization strategy is adopted in order to dampen the affects of instability incurred by a loss of orthogonality among the Lanczos vectors. Despite this however, round-off error still effects its performance particularly on the estimated Lanczos error bounds that are considerably different from the true error bound. In this paper a detailed analysis of the Lanczos error bound is presented and a new more realistic error proposed for determining a ‘good’ Ritz vector. A scheme is also proposed that uses this bound to derive start vectors for subsequent eigenpairs. The performance of the implementation of this scheme on the CRAY-T3E is critically assessed and some conclusions are drawn.
This work was carried out using the facilities of the University of Manchester Parallel Computing Centre
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© 2002 Springer-Verlag Berlin Heidelberg
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Cooper, A., Szularz, M., Weston, J. (2002). Analysis of the Lanczos Error Bounds and Its Application to the Explicitly Restarted Lanczos Algorithm. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2001. Lecture Notes in Computer Science, vol 2328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48086-2_46
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DOI: https://doi.org/10.1007/3-540-48086-2_46
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