A MATLAB implementation of matrix equation solvers.
Solves the matrix equation sum_j A{j} X B{j}^T = F for any number of terms, where A and B are cell arrays consisting of mxm and nxn matrices, respectively. The cost of the algorithm depends on the number of terms in the matrix equation. In particular, for more than 3 terms the cost is typically O((mn)^3) operations.
Solves the generalized Sylvester matrix equation given by
AXB' + CXD' = E
where A, C are mxm matrices, B and D are nxn matrices, and E is an mxn matrix. The algorithm is based on a generalization of Bartels-Stewart algorithm [1] and costs O(m^3+n^3) operations, see [2].
Solves the Lyapunov matrix equation given by A*X + X*A' + Q = 0, the Sylvester equation A*X + X*B + C = 0, and
the generalized Lyapunov equation A*X*E' + E*X*A' + Q = 0.
We do not claim that this is the best implementation of the Bartels-Stewart algorithm or that this is the best algorithm for solving AXB' + CXD' = E.
[1] R. H. Bartels & G. W. Stewart, Solution of the matrix equation AX +XB = C, Comm. ACM, 15, 820–826, 1972.
[2] J. D. Gardiner, A. J. Laub, J. J. Amato, & C. B. Moler, Solution of the Sylvester matrix equation AXB^T + CXD^T = E, ACM Transactions on Mathematical Software (TOMS), 18(2), 223-231, 1992.