A new algebraic majorization-minorization eigenvalue method

A parallel majorization and minorization of a Hamiltonian H (i.e., its energies E) is proposed as an improvement of the standard variational or perturbative techniques. It employs band matrices Hsub(0) (Hsub(0)sup((1)) = > H, Hsub(0)sup((2)) < = H) diagonalizable exactly by means of the analytic matrix continued fractions. The application of this general mathodical idea to the one-body problem with the anharmonic and Pade potentials is described in detail. A new, ''optimal'' computational algorithm is suggested whenever a smooth interpolation between Hsub(0)sup(1,2) exists