The accelerated overrelaxation splitting method for solving symmetric tensor equations

Abstract

This paper is concerned with solving the multilinear systems $${\mathscr {A}}\mathbf {x}^{m-1}=\mathbf {b}$$ whose coefficient tensors are mth-order and n-dimensional symmetric tensors. We first extend the accelerated overrelaxation (AOR) splitting method to solve the tensor equation. To improve the convergence, we develop a Newton-AOR (NAOR) method that hybridizes the Newton method and the accelerated overrelaxation scheme. Convergence analysis shows that the proposed methods converge under appropriate assumptions. Finally, some numerical examples are provided to show the effectiveness of the methods proposed.