| 四阶不完全对称张量M-特征值的新包含域及应用 |
| |
| 引用本文： | 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. |
| |
| 作者姓名： | 何军 刘衍民 许光俊 |
| |
| 作者单位： | 遵义师范学院数学学院, 遵义 563006 |
| |
| 基金项目： | 国家自然科学基金（11661084）资助. |
| |
| 摘 要： | 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.
|
| 关 键 词： | 四阶不完全对称张量 M-特征值 M-正定 |
| 收稿时间： | 2020-02-11 |
NEW M-EIGENVALUE INCLUSION SETS FOR FOURTH-ORDER PARTIALLY SYMMETRIC TENSORS WITH APPLICATIONS |
| |
| 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. |
| |
| Authors: | He Jun Liu Yanmin Xu Guangjun |
| |
| Institution: | School of Mathematics, Zunyi Normal college, Zunyi 563006, China |
| |
| Abstract: | 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. |
| |
| Keywords: | fourth-order partially symmetric tensor M-positive definiteness M-eigenvalue |
| 本文献已被 万方数据 等数据库收录！ |
| 点击此处可从《计算数学》浏览原始摘要信息 |
| 点击此处可从《计算数学》下载免费的PDF全文 |
|
