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

Qin Ni () and Liqun Qi ()

Journal of Global Optimization, 2015, vol. 61, issue 4, 627-641

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. Copyright Springer Science+Business Media New York 2015

Keywords: Nonnegative homogenous polynomial mapping; Nonnegative tensors; Eigenvalue of polynomial mapping; Newton method (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10898-014-0209-8

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