It is well known that the group of operators that commutes with the Hamiltonian operator can be used to facilitate the calculation of energy levels. Due to numerical errors in the computation of Hamiltonian matrix elements, it may happen that the matrix representation of a group operator does not commute with the Hamiltonian matrix although the group operator does commute with the Hamiltonian operator. We demonstrate that it is possible, even in this case, to use the single-symmetry and multisymmetry symmetry-adapted Lanczos (SAL) methods to efficiently compute energy levels. The two SAL methods are applied to the calculation of the bend levels of methane using the G(6) symmetry group and polyspherical angles. We show that although potential matrix elements are corrupted by quadrature error, it is nonetheless possible to take advantage of the full symmetry of the polyspherical basis. For a CX3Y-type molecule the symmetry-adapted method of this paper would enable one to exploit all of the symmetry of the molecule. (C) 2003 American Institute of Physics.