Numerical Methods for Solving Inverse Eigenvalue Problems for Nonnegative Matrices

Presented are two related numerical methods, one for the inverse eigenvalue problem for nonnegative or stochastic matrices and another for the inverse eigenvalue problem for symmetric nonnegative matrices. The methods are iterative in nature and utilize alternating projection ideas. For the symmetric problem, the main computational component of each iteration is an eigenvalue-eigenvector decomposition, while for the other problem, it is a Schur matrix decomposition. Numerical results are presented demonstrating the effectiveness of the algorithms. Keywords— Inverse eigenvalue problem, nonnegative matrices, stochastic matrices, alternating projections, Schur’s decomposition.