An alternate approach to expandingPA+A'P=-Q

The problem of expanding the matrix equation
PA + A'P = - Q
into a system of algebraic equations is considered. Starting from the previously published results, it suggests an alternate approach which is rather simple and very effective in computer applications. This approach is particularly useful when the given equation has to be solved iteratively which is the case in solution of the algebraic matrix Riccati equation appearing in optimal control problems.