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四阶不完全对称张量M-特征值的新包含域及应用

何军, 刘衍民, 许光俊   

  1. 遵义师范学院数学学院, 遵义 563006
  • 收稿日期:2020-02-11 出版日期:2021-11-14 发布日期:2021-11-12
  • 基金资助:
    国家自然科学基金(11661084)资助.

何军, 刘衍民, 许光俊. 四阶不完全对称张量M-特征值的新包含域及应用[J]. 计算数学, 2021, 43(4): 457-470.

He Jun, Liu Yanmin, Xu Guangjun. NEW M-EIGENVALUE INCLUSION SETS FOR FOURTH-ORDER PARTIALLY SYMMETRIC TENSORS WITH APPLICATIONS[J]. Mathematica Numerica Sinica, 2021, 43(4): 457-470.

NEW M-EIGENVALUE INCLUSION SETS FOR FOURTH-ORDER PARTIALLY SYMMETRIC TENSORS WITH APPLICATIONS

He Jun, Liu Yanmin, Xu Guangjun   

  1. School of Mathematics, Zunyi Normal college, Zunyi 563006, China
  • Received:2020-02-11 Online:2021-11-14 Published:2021-11-12
四阶不完全对称张量的M-特征值在非线性弹性材料分析中有着广泛的应用.本文的目的是给出四阶不完全对称张量M-特征值的新包含域,得到最大M-特征值上界更精确的估计,并将得到的上界估计值应用到计算最大M-特征值的WQZ算法中,数值例子验证了结果的有效性.最后,基于得到的包含域,给出了四阶不完全对称张量正定性判定的充分条件.
M-eigenvalues of a fourth-order partially symmetric tensor play an important role in the nonlinear elastic material analysis. In this paper, new M-eigenvalue inclusion sets for fourthorder partially symmetric tensors are established. As applications, upper bounds for the spectral radius of fourth-order partially symmetric tensors are obtained, these upper bounds are taken as the parameter in WQZ-algorithm. Finally, some veritable sufficient conditions of the M-positive definiteness for fourth-order partially symmetric tensors are given based on the M-eigenvalue inclusion sets.

MR(2010)主题分类: 

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