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- Title
A quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map.
- Authors
Ni, Qin; Qi, Liqun
- 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.
- Subjects
HOMOGENEOUS polynomials; NEWTON-Raphson method; QUADRATIC differentials; QUADRATIC transformations; SYMMETRIC functions
- Publication
Journal of Global Optimization, 2015, Vol 61, Issue 4, p627
- ISSN
0925-5001
- Publication type
Article
- DOI
10.1007/s10898-014-0209-8