  For one-dimensional systems with delta-contact interactions, the convergence
of the exact-diagonalization method is tested with a basis of harmonic
oscillator eigenfunctions with frequency $\Omega$ optimized through the
minimization of the eigenenergy of the desired level. It is shown that within
the framework of this approach the well-converged results can be achieved at
much smaller dimensions of the Hamiltonian matrix than with the standard
approach that uses $\Omega=1$. We present calculations for model systems of
identical bosons with harmonic and double-well potentials. Our results show
promising potential for diminishing the computational cost of numerical
simulations of various systems of trapped ultracold atoms.
