On the global Krylov subspace methods for solving general coupled matrix equations

In the present paper, we propose the global full orthogonalization method (GI-EOM) and global generalized minimum residual (GI-GMRES) method for solving large and sparse general coupled matrix equations Sigma(p)(j=1) A(ij)X(j)B(ij) = C-i, i = 1, ..., p, where A(ij) is an element of R-mxm, B-ij is an element of R-nxn, C-i is an element of R-mxn, i, j = 1,2, ..., p, are given matrices and X-i is an element of R-mxn, i = 1, 2, ..., p, are the unknown matrices. To do so, first, a new inner product and its corresponding matrix norm are defined. Then, using a linear operator equation and new matrix product, we demonstrate how to employ GI-FOM and GI-GMRES algorithms for solving general coupled matrix equations. Finally, some numerical experiments are given to illustrate the validity and applicability of the results obtained in this work. (C) 2011 Elsevier Ltd. All rights reserved.