Numerical approximation on computing partial sum of nonlinear Schrödinger eigenvalue problems

Abstract In computing electronic structure and energy band in the system of multiparticles, quite a large number of problems are to obtain the partial sum of the densities and energies by using “First principle”. In the ordinary method, the so-called self-consistency approach, the procedure is limited to a small scale because of its high computing complexity. In this paper, the problem of computing the partial sum for a class of nonlinear Schrodinger eigenvalue equations is changed into the constrained functional minimization. By space decomposition and Rayleigh-Schrodinger method, one approximating formula for the minimal is provided. The numerical experiments show that this formula is more precise and its quantity of computation is smaller.