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A nonmonotone accelerated Levenberg–Marquardt method for the B ‐eigenvalues of symmetric tensors
Author(s) -
Cao Mingyuan,
Yang Yueting,
Hou Tianliang,
Li Chaoqian
Publication year - 2022
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/itor.12954
Subject(s) - levenberg–marquardt algorithm , multilinear algebra , eigenvalues and eigenvectors , convergence (economics) , multilinear map , mathematics , mathematical optimization , algebra over a field , computer science , pure mathematics , jordan algebra , artificial neural network , artificial intelligence , physics , economics , current algebra , quantum mechanics , economic growth
The eigenvalues of tensors become more and more important in the numerical multilinear algebra. In this paper, based on the nonmonotone technique, an accelerated Levenberg–Marquardt (LM) algorithm is presented for computing the B ‐eigenvalues of symmetric tensors, in which an LM step and an accelerated LM step are computed at each iteration. We establish the global convergence of the proposed algorithm using properties of symmetric tensors and norms. Under the local error‐bound condition, the cubic convergence of the nonmonotone accelerated LM algorithm is derived. Numerical results show that this method is efficient.