An algorithm for constructing nonnegative matrices with prescribed real eigenvalues

Provided with the real spectrum, this paper presents a numerical procedure based on the induction principle to solve two types of inverse eigenvalue problems, one for nonnegative matrices and another for symmetric nonnegative matrices. As an immediate application, our approach can offer not only the sufficient condition to solve inverse eigenvalue problems for nonnegative or symmetric nonnegative matrices, but also a numerical way to solve inverse eigenvalue problems for stochastic matrices. Numerical examples are presented to show the capacity of our method.