Inversion of matrices with prescribed structured inverses

We present here a technique for the inversion of a matrix to an inverse with a prescribed structure. The approach is to generate a set of linear constraints that can then be optimized based on the resulting convex polytope. The approach is general and different error criteria can be implemented with minor modifications. The optimum is obtained as the center of mass of the polytope and it is shown that this result is best in the least-squares sense. Some properties of the algorithm are described and an example is submitted and discussed.