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This paper is concerned with regular approximations of spectra of singulardiscrete linear Hamiltonian systems with one singular endpoint. For any givenself-adjoint subspace extension (SSE) of the corresponding minimal subspace,its spectrum can be approximated by eigenvalues of a sequence of inducedregular SSEs, generated by the same difference expression on smaller finiteintervals. It is shown that every SSE of the minimal subspace has a purediscrete spectrum, and the k-th eigenvalue of any given SSE is exactly thelimit of the k-th eigenvalues of the induced regular SSEs; that is, spectralexactness holds, in the limit circle case. Furthermore, error estimates for theapproximations of eigenvalues are given in this case. In addition, in the limitpoint and intermediate cases, spectral inclusive holds.

Regular approximations of spectra of singular discrete linear Hamiltonian systems with one singular endpoint?