  The study of solving the inverse eigenvalue problem for nonnegative matrices
has been around for decades. It is clear that an inverse eigenvalue problem is
trivial if the desirable matrix is not restricted to a certain structure.
Provided with the real spectrum, this paper presents a numerical procedure,
based on the induction principle, to solve two kinds 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 for solving inverse eigenvalue problems for nonnegative or
symmetric nonnegative matrices, but also a quick numerical way to solve inverse
eigenvalue problem for stochastic matrices. Numerical examples are presented
for problems of relatively larger size.
