On Accurate Computations of the Perron Root
L. Elsner, I. Koltracht, Michael Neumann, Dong Xiao · SIAM Journal on Matrix Analysis and Applications · 1993
This paper establishes a new componentwise perturbation result for the Perron root of a nonnegative 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.