Partially doubly symmetric solutions of general Sylvester matrix equations

The study of linear matrix equations is extremely important in many scientific fields such as control systems and stability analysis. In this work, we aim to design the Hestenes-Stiefel (HS) version of biconjugate residual (Bi-CR) algorithm for computing the (least Frobenius norm) partially doubly symmetric solution X of the general Sylvester matrix equations Sigma(f)(j=1) A(ij)XB(ij) = M-i for i = 1, 2, ..., g. We show that the proposed algorithm converges in a finite number of iterations. Finally, numerical results compare the proposed algorithm to alternative algorithms.