LEAST-SQUARES APPROXIMATION BY REAL NORMAL MATRICES WITH SPECIFIED SPECTRUM

The problem of best approximating a given real matrix in the Frobenius norm by real, normal matrices subject to a prescribed spectrum is considered. The approach is based on using the projected gradient method. The projected gradient of the objective function on the manifold of constraints can be formulated explicity. This gives rise to a descent flow that can be followed numerically. The explicit form also facilitates the computation of the second-order optimality condition from which some interesting properties of the stationary points are related to the well-known Wielandt-Hoffman theorem.