Numerical subspace algorithms for solving the tensor equations involving Einstein product

In this article, we propose some subspace methods such as the conjugate residual, generalized conjugate residual, biconjugate gradient, conjugate gradient squared and biconjugate gradient stabilized methods based on the tensor forms for solving the tensor equation involving the Einstein product. These proposed algorithms keep the tensor structure. The convergence analysis shows that the proposed methods converge to the solution of the tensor equation for any initial value. Some numerical results confirm the feasibility and applicability of the proposed algorithms in practice.