Least squares solutions of the matrix equation AXB + CYD = E with the least norm for symmetric arrowhead matrices

In this paper, the least squares solution of the matrix equation AXB+CYD=E for symmetric arrowhead matrices with the least norm is discussed. By using Moore-Penrose inverse and the Kronecker product, the general expression of the solution to this problem is derived. A corresponding numerical algorithm and an example are also given.

[1]  Yuan Lei,et al.  Best Approximate Solution of Matrix Equation AXB+CYD=E , 2005, SIAM J. Matrix Anal. Appl..

[2]  David W. Lewis,et al.  Matrix theory , 1991 .

[3]  Xi-Yan Hu,et al.  The submatrix constraint problem of matrix equation AXB+CYD=E , 2009, Appl. Math. Comput..

[4]  Mehdi Dehghan,et al.  Finite iterative algorithms for the reflexive and anti-reflexive solutions of the matrix equation A1X1B1+A2X2B2=C , 2009, Math. Comput. Model..

[5]  G. Stewart,et al.  Computing the eigenvalues and eigenvectors of symmetric arrowhead matrices , 1990 .

[6]  Sang-Yeun Shim,et al.  LEAST SQUARES SOLUTION OF MATRIX EQUATION , 2003 .

[7]  Jan R. Magnus,et al.  L-structured matrices and linear matrix equations , 1983 .

[8]  M. Dehghan,et al.  The general coupled matrix equations over generalized bisymmetric matrices , 2010 .

[9]  Zhibing Liu,et al.  The Inverse Eigenvalue Problem for a Special Kind of Matrices , 2011, 2011 Fourth International Joint Conference on Computational Sciences and Optimization.

[10]  Yu Chen,et al.  Least Squares Solution of Matrix Equation AXB* + CYD* = E , 2002, SIAM J. Matrix Anal. Appl..

[11]  K. Chu,et al.  Singular value and generalized singular value decompositions and the solution of linear matrix equations , 1987 .

[12]  M. Baruch.  Optimal correction of mass and stiffness matrices using measured modes , 1982 .

[13]  Guoliang Chen,et al.  An iterative method for the symmetric and skew symmetric solutions of a linear matrix equation AXB+CYD=E , 2010, J. Comput. Appl. Math..

[14]  Guiping Xu,et al.  ON SOLUTIONS OF MATRIX EQUATION AXB + CYD = F , 1998 .