TY - JOUR
T1 - Convergence Analysis on SS-HOPM for BEC-Like Nonlinear Eigenvalue Problems
AU - Tang , Yaozong
AU - Yang , Qingzhi
AU - Luo , Gang
JO - Journal of Computational Mathematics
VL - 4
SP - 621
EP - 632
PY - 2021
DA - 2021/05
SN - 39
DO - http://doi.org/10.4208/jcm.2005-m2019-0298
UR - https://global-sci.org/intro/article_detail/jcm/19160.html
KW - nonlinear eigenvalues, Bose-Einstein Condensation, SS-HOPM, point-wise convergence, Lojasiewicz inequality.
AB - <p style="text-align: justify;">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.</p>