COMPARISON OF ERRORS IN UPPER AND LOWER BOUNDS TO EIGENVALUES OF SELF-ADJOINT EIGENVALUE PROBLEMS

The error in lower Lehmann bounds to eigenvalues of self-adjoint problems is estimated from above by a constant multiple of the error in corresponding, upper Rayleigh-Ritz bounds. The constant involved in explicitly computable and monotonically decreasing in the dimension of the approximate eigenvalue problems. Asymptotically, the same inequality holds for the general Lehmann-Goerisch approach. Numerical examples are included in order to investigate the accordance of computed error quotients and theoretical bounds.