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U. Helmke
or Runge-Kutta methods. Such a standard discretization method is however not recom-
mended, as it may lead to large errors in the eigenvalues. The difficulty with such an
approach is that the fixed eigenvalue constraints are not satisfied during the iterations.
Thus our goal is to find suitable approximations which preserve the isospectral nature of
the flow. Such approximate solutions are given by the geodesics of M(A). The geodesics of
the homogeneous space M(A) can be explicitly computed. They are of the form
et~Xe -t~ , X E
M(A)
where f~ is any skew-symmetric matrix in