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

作者：Li, Jiao-fen^*; Hu, Xi-yan; Zhang, Lei

来源：Numerical Linear Algebra with Applications, 2011, 18(5): 857-873.

DOI：10.1002/nla.771

• centrosymmetric matrix
• submatrix constraint
• iterative method
• least square problem
• perturbation analysis

We say that X = [x(ij)](i),(n)(j=1) is 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 parallel to AX B-C parallel to where parallel to.parallel to is the Frobenius norm, A is an element of R(mxn), B is an element of R(nxs), C is an element of R(mxs) and X is an element of R(nxn) 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.

• 出版日期2011-10
• 单位湖南大学; 桂林电子科技大学