The nearness problems for symmetric centrosymmetric with a special submatrix constraint

Abstract

We say that \(X=[x_{ij}]_{i,j=1}^n\) is symmetric centrosymmetric if xij = xji and xn − j + 1,n − i + 1, 1 ≤ i,j ≤ n. In this paper we present an efficient algorithm for minimizing ||AXAT − B|| where ||·|| is the Frobenius norm, A ∈ ℝm×n, B ∈ ℝm×m and X ∈ ℝn×n is symmetric centrosymmetric with a specified central submatrix [xij]p ≤ i,j ≤ n − p. Our algorithm produces a suitable X such that AXAT = B in finitely many steps, if such an X exists. We show that the algorithm is stable any case, and we give results of numerical experiments that support this claim.