A practical method for computing the largest M-eigenvalue of a fourth-order partially symmetric tensor
A practical method for computing the largest M-eigenvalue of a fourth-order partially symmetric tensor
复制标题
一种计算四阶部分对称张量最大M特征值的实用方法
DOI：
10.1002/nla.633
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发表时间：
2009-07-01
影响因子：
4.3
通讯作者：
Zhang, Xinzhen
中科院分区：
文献类型：
--
作者：
Wang, Yiju;Qi, Liqun;Zhang, Xinzhen
在本文中，我们考虑了在非线性弹性材料分析和量子物理中的纠缠研究中出现的两个单位球面上的双二次齐次多项式优化问题。这个问题等价于计算一个四阶张量的最大M-特征值。为了解决这个问题，我们提出了一种实用的方法，从理论上保证了该方法的有效性。为了使该方法生成的序列收敛于问题的良好解，我们还开发了一种初始化方案。给出的数值实验表明了该方法的有效性。版权所有(C)2009 John Wiley&Sons，Ltd.
In this paper, we consider a bi-quadratic homogeneous polynomial optimization problem over two unit spheres arising in nonlinear elastic material analysis and in entanglement studies in quantum physics. The problem is equivalent to computing the largest M-eigenvalue of a fourth-order tensor. To solve the problem, we propose a practical method whose validity is guaranteed theoretically. To make the sequence generated by the method converge to a good solution of the problem, we also develop an initialization scheme. The given numerical experiments show the effectiveness of the proposed method. Copyright (C) 2009 John Wiley & Sons, Ltd.