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.

引用

页码：627 / 641

页数：14