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

We say that X = [ x ij ]   n i, j = 1is centrosymmetric if x ij = x n − j + 1, n − i + 1 , 1⩽ i, j ⩽ n . In this paper, we present an efficient algorithm for minimizing ∥ AXB − C ∥ where ∥·∥ is the Frobenius norm, A ∈ℝ m × n , B ∈ℝ n × s , C ∈ℝ m × s and X ∈ℝ n × n is centrosymmetric with a specified central submatrix [ x ij ] p ⩽ i, j ⩽ n − p . Our algorithm produces a suitable X such that AXB = 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.