Iterative algorithms for solving some tensor equations

Abstract

ABSTRACTWe propose a class of iterative algorithms to solve some tensor equations via Einstein product. These algorithms use tensor computations with no matricizations involved. For any (special) initial tensor, a solution (the minimal Frobenius norm solution) of related problems can be obtained within finite iteration steps in the absence of roundoff errors. Numerical examples are provided to confirm the theoretical results, which demonstrate that this kind of iterative methods are effective and feasible for solving some tensor equations.