Saeed Karimi

In this paper, the linear matrix equation AXB = C is considered, where A ? Rn×m, B ? Rq×s are given large matrices and C ? Rn×s, X ? Rm×q are right-hand side and unknown matrices, respectively. The global least squares algorithm is applied to approximate the solution of this group of matrix equations. The right–left preconditioned global least squares algorithm is presented for obtaining the approximate solution of the mentioned matrix equation. This preconditioner is based on the C-orthogonalization process, where C is a symmetric positive definite matrix. Also, the iterative method and its preconditioned algorithm are proposed to find the approximate generalized inverses of nearly singular matrices and rectangular matrices. Finally, some numerical experiments are given to illustrate the efficiency of the new preconditioners.