An iterative algorithm for the least squares bisymmetric solutions of the matrix equations A1XB1=C1, A2XB2=C2

@article{Cai2009AnIA,
  title={An iterative algorithm for the least squares bisymmetric solutions of the matrix equations A1XB1=C1, A2XB2=C2},
  author={Jing Cai and Guoliang Chen},
  journal={Mathematical and Computer Modelling},
  year={2009},
  volume={50},
  pages={1237-1244}
}
In this paper, an iterative algorithm is constructed to solve the minimum Frobenius norm residual problem: min ∥∥∥(A1XB1 A2XB2)− (C1 C2)∥∥∥ over bisymmetric matrices. By this algorithm, for any initial bisymmetric matrix X0, a solution X can be obtained in finite iteration steps in the absence of roundoff errors, and the solution with least norm can be obtained by choosing a special kind of initial matrix. Furthermore, in the solution set of the above problem, the unique optimal approximation… CONTINUE READING
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