  We propose a variational perturbation method based on the observation that
eigenvalues of each parity sector of both the anharmonic and double-well
oscillators are approximately equi-distanced. The generalized deformed algebra
satisfied by the invariant operators of the systems provides well defined
Hilbert spaces to both of the oscillators. There appears a natural expansion
parameter defined by the ratios of three distance scales of the trial
wavefunctions. The energies of the ground state and the first order excited
state, in the $0^{th}$ order variational approximation, are obtained with
errors $<10^{-2}$% for vast range of the coupling strength for both
oscillators. An iterative formula is presented which perturbatively generates
higher order corrections from the lower order invariant operators and the first
order correction is explicitly given.
