The submatrix constraint problem of matrix equation AXB plus CYD = E

We say that X = [x(ij)](i,j-1)(n) is symmetric centrosymmetric if x(ij) = x(ji) and x(n-j+1,n-i+1), 1 <= i,j <= n. In this paper we present an efficient algorithm for minimizing parallel to AXB + CYD - E parallel to where parallel to.parallel to is the Frobenius norm, A is an element of R-txn, B is an element of R-nxs, C is an element of R-txm, D is an element of R-mxs, E is an element of R-txs and X is an element of R-nxn is symmetric centrosymmetric with a specified central submatrix [x(ij)](r <= i,j <= n-r), Y is an element of R-mxm is symmetric with a specified central submatrix [y(ij)](1 <= i,j <= p). Our algorithm produces suitable X and Y such that AXB + CYD E in finitely many steps, if such X and Y exists. We show that the algorithm is stable any case, and we give results of numerical experiments that support this claim. (C) 2009 Elsevier Inc. All rights reserved.