Journal of Shanghai University(Natural Science Edition) ›› 2017, Vol. 23 ›› Issue (1): 68-72.doi: 10.3969/j.issn.1007-2861.2016.07.009

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A preconditioning iterative algorithm for eigenvalue problem of symmetric tensor

GU Chuanqing, LI Long   

  1. College of Sciences, Shanghai University, Shanghai 200444, China
  • Received:2016-12-05 Online:2017-02-28 Published:2017-02-28

Abstract:

Shifted symmetric high order power method (SS-HOPM) is a well-known iterative algorithm for solving tensor Z-eigenvalue. In this paper, the Newton method is used to deal with the initial condition of the algorithm. A Newton preconditioning SS-HOPM(PSS-HOPM) for the symmetric tensor eigenvalue problem is obtained. Two numerical examples are used to illustrate that, compared with the SS-HOPM algorithm, this algorithm can calculate more eigenvalues with little increase of computation time.

Key words: Newton method , Newton preconditioned method, shifted symmetric high order power method (SS-HOPM)