Normalized Newton method to solve generalized tensor eigenvalue problems

Abstract

The problem of generalized tensor eigenvalue is the focus of this paper. To solve the problem, we suggest using the normalized Newton generalized eigenproblem approach (NNGEM). Since the rate of convergence of the spectral gradient projection method (SGP), the generalized eigenproblem adaptive power (GEAP), and other approaches is only linear, they are significantly improved by our proposed method, which is demonstrated to be locally and cubically convergent. Additionally, the modified normalized Newton method (MNNM), which converges to symmetric tensors Z-eigenpairs under the same $\gamma$-Newton stability requirement, is extended by the NNGEM technique. Using a Gröbner basis, a polynomial system solver (NSolve) generates all of the real eigenvalues for us. To illustrate the efficacy of our methodology, we present a few numerical findings.