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

We say that X = [xij] is centrosymmetric if xij = xn − 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∈ℝm × n, B∈ℝn × s, C∈ℝm × s and X∈ℝn × n is centrosymmetric with a specified central submatrix [xij]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.

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