Extending BiCG and BiCR methods to solve the Stein tensor equation

The biconjugate gradients (BiCG) and biconjugate residual (BiCR) methods are attractive ways for solving nonsymmetric linear system $Ax=b$. In this paper, the BiCG and BiCR methods are extended to solve the high order Stein tensor equation. The convergent properties of the developed iterative algorithms are studied. Numerical examples are provided to confirm the theoretical results, which demonstrate that the proposed algorithms are effective and feasible for solving the Stein tensor equation.