*Title*: **Two iterative methods for a generalized eigenvalue problem following Perron-Frobenius Theory**

*Abstract*: We consider a matrix pair (A,B) that can be transformed to
a nonnegative matrix. Such a matrix pair has a real eigenvalue
on the interval (0,1) and a corresponding eigenvector with
positive components. We developed two iterative methods
for computing this eigenpair. Both methods are generalized
versions of the Noda iteration for nonnegative matrices.
both methods converge quadratically. Comparisons are
made with some numerical examples.
This is a joint work with X. Chen, W. Li (S. China Normal)
and S. Vong (Macau).

CAM Seminar Fall 2017 - Spring 2018