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Volume 39, Issue 4
Convergence Analysis on SS-HOPM for BEC-Like Nonlinear Eigenvalue Problems

Yaozong Tang, Qingzhi Yang & Gang Luo

DOI: 10.4208/jcm.2005-m2019-0298

J. Comp. Math., 39 (2021), pp. 621-632.

Published online: 2021-05

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  • 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.

  • Keywords

nonlinear eigenvalues, Bose-Einstein Condensation, SS-HOPM, point-wise convergence, Lojasiewicz inequality.

  • AMS Subject Headings

15A18,15A69,90C26

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

tangyz_1982@163.com (Yaozong Tang)

qz-yang@nankai.edu.cn (Qingzhi Yang)

luogang@gmail.com (Gang Luo)

  • BibTex
  • RIS
  • TXT
@Article{JCM-39-621, author = {Tang , YaozongYang , Qingzhi and Luo , Gang}, title = {Convergence Analysis on SS-HOPM for BEC-Like Nonlinear Eigenvalue Problems}, journal = {Journal of Computational Mathematics}, year = {2021}, volume = {39}, number = {4}, pages = {621--632}, 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2005-m2019-0298}, url = {http://global-sci.org/intro/article_detail/jcm/19160.html} }
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 -

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.

Tang , YaozongYang , Qingzhi and Luo , Gang. (2021). Convergence Analysis on SS-HOPM for BEC-Like Nonlinear Eigenvalue Problems. Journal of Computational Mathematics. 39 (4). 621-632. doi:10.4208/jcm.2005-m2019-0298
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