  An efficient method to compute magnetic exchange interactions in systems with
strong correlations is introduced. It is based on a magnetic force theorem
which evaluates linear response due to rotations of magnetic moments and uses a
novel spectral density functional framework combining our exact diagonalization
based dynamical mean field and local density functional theories. Applications
to spin waves and magnetic transition temperatures of 3d metal mono--oxides as
well as high--T_{c} superconductors are in good agreement with experiment.
