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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Qin Ni

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong

    Liqun Qi

Authors
  1. Qin Ni
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  2. Liqun Qi
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Correspondence to Qin Ni.

Additional information

Qin Ni: His work was supported by National Science Foundation of China (11071117) and Jiangsu Province (SBK2014020180).

Liqun Qi: His work was supported by the Hong Kong Research Grant Council (Grant No. PolyU 501909, 502510, 502111 and 501212).

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Ni, Q., Qi, L. A quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map. J Glob Optim 61, 627–641 (2015). https://doi.org/10.1007/s10898-014-0209-8

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  • DOI: https://doi.org/10.1007/s10898-014-0209-8

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