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We discuss a novel strategy for computing the eigenvalues and eigenfunctionsof the relativistic Dirac operator with a radially symmetric potential. Thevirtues of this strategy lie on the fact that it avoids completely thephenomenon of spectral pollution and it always provides two-side estimates forthe eigenvalues with explicit error bounds on both eigenvalues andeigenfunctions. We also discuss convergence rates of the method as well asillustrate our results with various numerical experiments.

Non-variational computation of the eigenstates of Dirac operators with radially symmetric potentials