  We introduce various optimization schemes for highly accurate calculation of
the eigenvalues and the eigenfunctions of the one-dimensional anharmonic
oscillators. We present several methods of analytically fixing the nonlinear
variational parameter specified by the domain of the trigonometric basis
functions. We show that the optimized parameter enables us to determine the
energy spectrum to an arbitrary accuracy. Also, using the harmonic oscillator
basis functions, we indicate that the resulting optimal frequency agrees with
the one obtained by the principle of the minimal sensitivity.
