  We compare the well known Rayleigh-Ritz variational method (RRVM) with a
recently proposed approach based on supersymmetric quantum mechanics and the
Gram-Schmidt orthogonalization method (SSQMGS). We apply both procedures to a
particular class of double-well harmonic oscillators that had been conveniently
chosen for the application of the latter approach. The RRVM eigenvalues
converge smoothly from above providing much more accurate results with less
computational effort. Present results show that the unproved SSQMGS upper
bounds do not hold.
