  In this article we study the estimation of bifurcation coefficients in
nonlinear branching problems by means of Rayleigh-Ritz approximation to the
eigenvectors of the corresponding linearized problem. It is essential that the
approximations converge in a norm of sufficient strength to render the
nonlinearities continuous. Quadratic interpolation between Hilbert spaces is
used to seek sharp rate of convergence results for bifurcation coefficients.
Examples from ordinary and partial differential problems are presented.
