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Finding the extreme Z‐eigenvalues of tensors via a sequential semidefinite programming method
Author(s) -
Hu Shenglong,
Huang ZhengHai,
Qi Liqun
Publication year - 2013
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1884
Subject(s) - mathematics , eigenvalues and eigenvectors , semidefinite programming , conic section , tensor (intrinsic definition) , generalization , dimension (graph theory) , sequence (biology) , mathematical optimization , algebra over a field , mathematical analysis , pure mathematics , physics , geometry , quantum mechanics , biology , genetics
SUMMARY In this paper, we first introduce the tensor conic linear programming (TCLP), which is a generalization of the space TCLP. Then an approximation method, by using a sequence of semidefinite programming problems, is proposed to solve the TCLP. In particular, we reformulate the extreme Z‐eigenvalue problem as a special TCLP. It gives a numerical algorithm to compute the extreme Z‐eigenvalue of an even order tensor with dimension larger than three, which improves the literature. Numerical experiments show the efficiency of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.