D.L. Vinokursky, V.A. Galkina

In this paper, the theory of recursion methods are discussed within an orthogonal basis in Krylov-s subspace. Then, as an extension of the recursion method, are practical recursion method based on the Lanczos algorithm are presented. Several convergence properties for energies and forces show that the block scheme handles automatically. Our use of the Lanczos basis simplifies the calculation of the band energy and forces, which allows the application of the methods to the density functional theory and molecular dynamics simulation of the very large system.