CONSTRUCTING SYMMETRICAL NONNEGATIVE MATRICES WITH PRESCRIBED EIGENVALUES BY DIFFERENTIAL-EQUATIONS

The inverse eigenvalue problem is solved for symmetric nonnegative matrices by means of a differential equation. If the given spectrum is feasible, then a symmetric nonnegative matrix can be constructed simply by following the solution curve of the differential system. The choice of the vector field 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. The projected gradient of the objective function is explicitly described. Using center manifold theory, it is also shown that the omega-limit set of any solution curve is a single point. Some numerical examples are presented.