A quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map

被引：0
|
作者：
Qin Ni
Liqun Qi
机构：
[1] Nanjing University of Aeronautics and Astronautics,Department of Mathematics
[2] The Hong Kong Polytechnic University,Department of Applied Mathematics
来源：
Journal of Global Optimization | 2015年 / 61卷
关键词：
Nonnegative homogenous polynomial mapping; Nonnegative tensors; Eigenvalue of polynomial mapping; Newton method;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：627 / 641
页数：14
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