A quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map
A quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map
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DOI：
10.1007/s10898-014-0209-8
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发表时间：
2014-06
影响因子：
1.8
通讯作者：
Q. Ni;L. Qi
中科院分区：
文献类型：
--
作者：
Q. Ni;L. Qi
本文提出了一种求非负齐次多项式映射最大特征值的二次收敛算法，其中用牛顿法求解一个等价的非线性方程组。引入半对称张量来揭示齐次多项式映射与其对应的半对称张量之间的关系。基于这种关系，建立了插入线搜索的全局二次收敛算法。文中给出了该方法的一些数值结果。
In this paper we propose a quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map where the Newton method is used to solve an equivalent system of nonlinear equations. The semi-symmetric tensor is introduced to reveal the relation between homogeneous polynomial map and its associated semi-symmetric tensor. Based on this relation a globally and quadratically convergent algorithm is established where the line search is inserted. Some numerical results of this method are reported.