A Levenberg–Marquardt method for solving semi-symmetric tensor equations

Abstract

In this paper, we propose a Levenberg–Marquardt (LM) method for solving tensor equations with semi-symmetric coefficient tensor and prove its global convergence and local quadratic convergence under the local error bound condition, which is weaker than non-singularity. As application, we solve H-eigenvalue of real semi-symmetric tensor by the LM method. At last, some numerical examples are provided to illustrate the efficiency and validity of these methods proposed.