Constructing Symmetric Nonnegative Matrices with Prescribed Eigenvalues by Di erential Equations

We propose solving the inverse eigenvalue problem for symmetric nonnegative matrices by means of a di erential equation. If the given spectrum is feasible, then a symmetric nonnegative matrix can be constructed simply by following the solution curve of the di erential system. The choice of the vector eld is based on the idea of minimizing the distance between the cone of symmetric nonnegative matrices and the isospectral surface determined by the given spectrum. We explicitly describe the projected gradient of the objective function. Using center manifold theory, we also show that the !-limit set of any solution curve is a single point. Some numerical examples are presented.