  We systematically improve the recent variational calculation of the imaginary
part of the ground state energy of the quartic anharmonic oscillator.
  The results are extremely accurate as demonstrated by deriving, from the
calculated imaginary part, all perturbation coefficients via a dispersion
relation and reproducing the exact values with a relative error of less than
$10^{-5}$. A comparison is also made with results of a Schr\"{o}dinger
calculation based on the complex rotation method.
