Developing BiCOR and CORS methods for coupled Sylvester-transpose and periodic Sylvester matrix equations

Recently the biconjugate A-orthogonal residual (BiCOR) and the conjugate A-orthogonal residual squared (CORS) methods have been introduced for solving nonsymmetric linear systems Ax=b. This study directly develops the BiCOR and CORS methods to obtain matrix iterative methods for solving the coupled Sylvester-transpose matrix equations∑k=1l(A1,kXB1,k+C1,kXTD1,k+E1,kYF1,k)=M1,∑k=1l(A2,kXB2,k+C2,kXTD2,k+E2,kYF2,k)=M2,and the coupled periodic Sylvester matrix equationsA1,jXjB1,j+C1,jXj+1D1,j+E1,jYjF1,j=M1,j,A2,jXjB2,j+C2,jXj+1D2,j+E2,jYjF2,j=M2,j,forj=1,2,…,μ.Numerical examples are given at the end of this paper to compare the accuracy and efficiency of the matrix iterative methods with other methods in the literature.