Convergence Analysis on SS-HOPM for BEC-Like Nonlinear Eigenvalue Problems

Abstract

Shifted symmetric higher-order power method (SS-HOPM) has been proved effective in solving the nonlinear eigenvalue problem oriented from the Bose-Einstein Condensation (BEC-like NEP for short) both theoretically and numerically. However, the convergence of the sequence generated by SS-HOPM is based on the assumption that the real eigenpairs of BEC-like NEP are finite. In this paper, we will establish the point-wise convergence via Lojasiewicz inequality by introducing a new related sequence.