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The study of solving the inverse eigenvalue problem for nonnegative matriceshas been around for decades. It is clear that an inverse eigenvalue problem istrivial 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 eigenvalueproblems, one for nonnegative matrices and another for symmetric nonnegativematrices. As an immediate application, our approach can offer not only thesufficient condition for solving inverse eigenvalue problems for nonnegative orsymmetric nonnegative matrices, but also a quick numerical way to solve inverseeigenvalue problem for stochastic matrices. Numerical examples are presentedfor problems of relatively larger size.

A fast numerical algorithm for constructing nonnegative matrices with prescribed real eigenvalues