  We have introduced the generalized alternating direction implicit iteration
(GADI) method for solving large sparse complex symmetric linear systems and
proved its convergence properties. Additionally, some numerical results have
demonstrated the effectiveness of this algorithm. Furthermore, as an
application of the GADI method in solving complex symmetric linear systems, we
utilized the flattening operator and Kronecker product properties to solve
Lyapunov and Riccati equations with complex coefficients using the GADI method.
In solving the Riccati equation, we combined inner and outer iterations, first
simplifying the Riccati equation into a Lyapunov equation using the Newton
method, and then applying the GADI method for solution. Finally, we provided
convergence analysis of the method and corresponding numerical results.
