An adaptive gradient method for computing generalized tensor eigenpairs

High order tensor arises more and more often in signal processing, data analysis, higher-order statistics, as well as imaging sciences. In this paper, an adaptive gradient (AG) method is presented for generalized tensor eigenpairs. Global convergence and linear convergence rate are established under some suitable conditions. Numerical results are reported to illustrate the efficiency of the proposed method. Comparing with the GEAP method, an adaptive shifted power method proposed by Kolda and Mayo (SIAM J Matrix Anal Appl 35:1563---1581, 2014) the AG method is much faster and could reach the largest eigenpair with a higher probability.