  The ground and excited states of a weakly interacting and dilute
Bose-Einstein condensed gas, confined in a completely anisotropic harmonic
oscillator potential, are determined at zero temperature within the Bogoliubov
approximation. The numerical calculations employ a computationally efficient
procedure based on a discrete variable representation (DVR) of the Hamiltonian.
The DVR is efficient for problems where the interaction potential may be
expressed as a local function of interparticle coordinates. In order to address
condensates that are both very large (millions of atoms) and fully anisotropic,
the ground state is found using a self-consistent field approach. Experience
has demonstrated, however, that standard iterative techniques applied to the
solution of the non-linear partial differential equation for the condensate are
non-convergent. This limitation is overcome using the method of direct
inversion in the iterated subspace (DIIS). In addition, the sparse structure of
the DVR enables the efficient application of iterative techniques such as the
Davidson and/or Lanczos methods, to extract the eigenvalues of physical
interest. The results are compared with recent experimental data obtained for
Bose-Einstein condensed alkali metal vapors confined in magnetic traps.
