Numerical solutions of AXB = C for centrosymmetric matrix X under a specified submatrix constraint

We say that X = [xi j ]n i, j=1 is centrosymmetric if xi j = xn− j+1,n−i+1, 1 i, j n. In this paper, we present an efficient algorithm for minimizing ‖AX B−C‖ where ‖·‖ is the Frobenius norm, A∈Rm×n , B∈ Rn×s , C ∈Rm×s and X ∈Rn×n is centrosymmetric with a specified central submatrix [xi j ]p i, j n−p . Our algorithm produces a suitable X such that AX B=C in finitely many steps, if such an X exists. We show that the algorithm is stable in any case, and we give results of numerical experiments that support this claim. Copyright 2011 John Wiley & Sons, Ltd.