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Classes of admissible potentials include electromagnetic potentials with strong Coulomb singularities and more general matrix-valued potentials, even non-self-adjoint ones. For the Coulomb potential, we achieve an exact diagonalization up to nuclear charge Z=124 and prove the convergence of the Douglas-Kroll-He\\ss\\ approximation up to Z=62, thus improving the upper bounds Z=93 and Z=51, respectively, by H.\\ Siedentop and E.\\ Stockmeyer considerably. 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