Solving tensor absolute value equation

Abstract In this paper, we analyze the existence of solutions of tensor absolute value equation (TAVE) and propose a SOR-type iteration algorithm for solving this equation. First, we introduce the interval tensor, which is the main tool for proving the unique solvability of TAVE. Then we present a sufficient condition for TAVE to have a unique solution. Furthermore, we propose a SOR-type iteration algorithm for solving TAVE. The convergence of the proposed algorithm is analysed under suitable assumptions. Finally, numerical experiments illustrate that our algorithm is feasible and effective.