Convergence Analysis on SS-HOPM for BEC-Like Nonlinear Eigenvalue Problems (Journal of Computational Mathematics, 2021)
Shifted symmetric higher-order power method (SS-HOPM) has been proved effectivein solving the nonlinear eigenvalue problem oriented from the Bose-Einstein Condensation(BEC-like NEP for short) both theoretically and numerically. However, the convergence ofthe sequence generated by SS-HOPM is based on the assumption that the real eigenpairsof BEC-like NEP are finite. In this paper, we will establish the point-wise convergence via Lojasiewicz inequality by introducing a new related sequence.
Keywords: nonlinear eigenvalues; Bose-Einstein Condensation; SS-HOPM; point-wise convergence; Lojasiewicz inequality.