Runge Kutta type methods for isodynamical matrix flows: applications to balanced realizations

Recently several numerical methods have been proposed for solving isospectral problems which are matrix differential systems whose solutions preserve the spectrum during the evolution. In this paper we consider matrix differential systems called isodynamical flows in which only a component of the matrix solution preserves the eigenvalues during the evolution and we propose procedures for their numerical solution. Applications of such numerical procedures may be found in systems theory, in particular in balancing realization problems. Several numerical tests will be reported.