A nonmonotone accelerated Levenberg–Marquardt method for the ‐eigenvalues of symmetric tensors

Abstract

AbstractThe 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 ‐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.