An adaptive gradient method for computing generalized tensor eigenpairs

TL;DR

This paper introduces an adaptive gradient method for efficiently computing generalized tensor eigenpairs, demonstrating faster convergence and higher success probability compared to existing methods.

Contribution

The paper proposes a novel adaptive gradient method with proven convergence properties for tensor eigenpair computation, outperforming previous algorithms in speed and accuracy.

Findings

The AG method converges globally and linearly under certain conditions.

Numerical results show the AG method is faster than existing methods.

The AG method has a higher probability of reaching the largest eigenpair.

Abstract

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 Tamara G. Kolda and Jackson R. Mayo [SIAM J. Matrix Anal. Appl., 35 (2014), pp. 1563-1581], the AG method is much faster and could reach the largest eigenpair with a higher probability.