Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 627-641 |
| Number of pages | 15 |
| Journal | Journal of Global Optimization |
| Volume | 61 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 22 Mar 2015 |
Keywords
- Eigenvalue of polynomial mapping
- Newton method
- Nonnegative homogenous polynomial mapping
- Nonnegative tensors
ASJC Scopus subject areas
- Computer Science Applications
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics