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).