id: 06041749
dt: j
an: 06041749
au: Liang, Kaifu; Liu, Jianzhou
ti: The least squares symmetric-skew symmetric solution of the generalized
    coupled Sylvester matrix equations.
so: Math. Appl. 24, No. 4, 746-753 (2011).
py: 2011
pu: Editorial Board of Mathematica Applicata, Huazhong University of Science
    and Technology, Wuhan
la: ZH
cc: 
ut: matrix equation; iterative method; least-squares solution; symmetric-skew
    symmetric solution; minimum residual problem; algorithm; normal matrix
    equations
ci: 
li: 
ab: Summary: An iterative method is proposed for solving the minimum residual
    $$\left\|\,\pmatrix A_1XB_1+C_1YD_1\\A_2XB_2+C_2YD_2\endpmatrix
    -\pmatrix M_1\\M_2\endpmatrix \,\right\|=\min$$ over $X$ symmetric and
    $Y$ skew symmetric-matrices. Firstly, we obtain that the normal
    equations are equivalent to the minimum residual problem, and then an
    iterative algorithm is presented for solving the normal matrix
    equations. By using the iterative method, the least squares
    symmetric-skew symmetric solution can be got within finite iteration
    steps in the absence of roundoff errors for any initial symmetric-skew
    symmetric matrix pair $(X_0,Y_0)$. Moreover, the least squares
    symmetric-skew symmetric solution with minimum norm can be got by
    choosing a special kind of the initial matrix.
rv: