On accurate computations of the Perron root
Elsner L, Koltracht I, Neumann M, Xiao D (1993)
SIAM Journal on matrix analysis and applications 14(2): 456-467.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Autor*in
Elsner, LudwigUniBi;
Koltracht, Israel;
Neumann, Michael;
Xiao, D.
Einrichtung
Abstract / Bemerkung
This paper establishes a new componentwise perturbation result for the Perron root of a non-negative and irreducible matrix. The error bound is independent of the angle between left and right Perron eigenvectors. It is shown that a known inverse iteration algorithm with new stopping criteria will have a small componentwise backward error, which is consistent with the perturbation result. Numerical experiments demonstrate that the accuracy of the Perron root computed by the proposed algorithm is, indeed, independent of the angle.
Stichworte
Nonnegative matrices;
Componentwise perturbations;
Perron root;
Stable algorithms;
Backward error;
Sparse systems
Erscheinungsjahr
1993
Zeitschriftentitel
SIAM Journal on matrix analysis and applications
Band
14
Ausgabe
2
Seite(n)
456-467
ISSN
0895-4798
eISSN
1095-7162
Page URI
https://pub.uni-bielefeld.de/record/1776225
Zitieren
Elsner L, Koltracht I, Neumann M, Xiao D. On accurate computations of the Perron root. SIAM Journal on matrix analysis and applications. 1993;14(2):456-467.
Elsner, L., Koltracht, I., Neumann, M., & Xiao, D. (1993). On accurate computations of the Perron root. SIAM Journal on matrix analysis and applications, 14(2), 456-467. https://doi.org/10.1137/0614032
Elsner, Ludwig, Koltracht, Israel, Neumann, Michael, and Xiao, D. 1993. “On accurate computations of the Perron root”. SIAM Journal on matrix analysis and applications 14 (2): 456-467.
Elsner, L., Koltracht, I., Neumann, M., and Xiao, D. (1993). On accurate computations of the Perron root. SIAM Journal on matrix analysis and applications 14, 456-467.
Elsner, L., et al., 1993. On accurate computations of the Perron root. SIAM Journal on matrix analysis and applications, 14(2), p 456-467.
L. Elsner, et al., “On accurate computations of the Perron root”, SIAM Journal on matrix analysis and applications, vol. 14, 1993, pp. 456-467.
Elsner, L., Koltracht, I., Neumann, M., Xiao, D.: On accurate computations of the Perron root. SIAM Journal on matrix analysis and applications. 14, 456-467 (1993).
Elsner, Ludwig, Koltracht, Israel, Neumann, Michael, and Xiao, D. “On accurate computations of the Perron root”. SIAM Journal on matrix analysis and applications 14.2 (1993): 456-467.
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