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 (CURS) methods have been introduced for solving nonsymmetric linear systems Ax = b. This study directly develops the BiCOR and CURS methods to obtain matrix iterative methods for solving the coupled Sylvester-transpose matrix equations {Sigma(1)(K=1)(A(1,k)XB(1,k) + (C1,kXD1,k)-D-T + E1,kYF1,k) = M-1, Sigma(1)(K=1)(A(2,k)XB(1,k) + (C2,kXD2,k)-D-T + E2,kYF2,k) = M-2, and the coupled periodic Sylvester matrix equations {A(1,j)X(j)B(1,j) + C1,jXj+1D1,j + epsilon 1,jYjF1,j = M-1,M-j, for j = 1,2,....mu. A(2,j)X(j)B(2,j) + C2,jXj+1D2,j + epsilon 2,jYjF2,j = M-2,M-j, 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. (C) 2015 Elsevier Inc. All rights reserved.