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.

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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.
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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.
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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