A class of optimal solutions of the matrix Nehari‐extension problem

The degrees of freedom that are available in the solution set of the multivariable Nehari‐extension problem are used to minimize an 2 ‐type cost and an ‘entropy‐like’ cost associated with the smaller singular values of the (optimal) error system. The optimal extensions are constructed via a diagonalization procedure based on a (normalized) Schmidt pair of the Hankel operator induced by the function which is approximated.