Efficient Low-Rank Generalized Alternating Direction Implicit Iteration Method for Solving Large-Scale Matrix Equations

This paper presents an effective low-rank generalized alternating direction implicit iteration (R-GADI) method for efficiently solving large-scale sparse and stable Lyapunov matrix equations and continuous-time algebraic Riccati matrix equations. The method exploits the low-rank property of matrices and utilizes Cholesky factorization, providing a direct and efficient low-rank formulation that saves storage space and computational cost.