We present a numerically accurate procedure for the study of the electronic structure of one-dimensional incommensurate systems. Our method is used to infer the localized or extended nature of the electronic states by considering, at the same time, both diagonal and off-diagonal matrix elements of an appropriate effective Hamiltonian; we work out a convenient expression of the Lyapunov coefficient in terms of the off-diagonal effective matrix elements. With the further implementation of separately processing (though interdependently) the appropriate segments of the infinite chain, we provide a simple method to reach any desired numerical precision, so that physical aspects can be clearly worked out. Our procedure is tested on an incommensurate potential that exhibits mobility edges.