The spectral moments method

A systematic analysis of the spectral moments method is presented and developed to compute the response functions of very large harmonic systems. Convergence of the algorithms is discussed and solutions are proposed to improve the results obtained. New developments are proposed. They concern, on the one hand, the determination of the Green functions or correlation functions of the system, and the localization of eigenvectors and, on the other hand, the determination of the spectral density of very large homogeneous matrices by a very simple and powerful technique. These results are illustrated by several examples taken from the main subjects studied by the authors: conducting polymers, fractals and quasi-crystals. Then comparison with other methods is discussed.