A Levenberg-Marquardt method for solving semi-symmetric tensor equations
A Levenberg-Marquardt method for solving semi-symmetric tensor equations
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DOI：
10.1016/j.cam.2017.10.005
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发表时间：
2018-04
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影响因子：
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通讯作者：
Chang-Qing Lv;Changfeng Ma
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文献类型：
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作者：
Chang-Qing Lv;Changfeng Ma
本文提出了一种求解具有半对称系数张量的张量方程的Levenberg-Marquardt（LM）方法，并在比非奇异性弱的局部误差界条件下证明了其全局收敛性和局部二次收敛性.作为应用，我们用LM方法求解了真实的半对称张量的H-特征值。最后通过数值算例说明了所提方法的有效性。
In this paper, we propose a Levenberg–Marquardt (LM) method for solving tensor equations with semi-symmetric coefficient tensor and prove its global convergence and local quadratic convergence under the local error bound condition, which is weaker than non-singularity. As application, we solve H-eigenvalue of real semi-symmetric tensor by the LM method. At last, some numerical examples are provided to illustrate the efficiency and validity of these methods proposed.