A Low-rank ADI Algorithm for the Numerical Solution of Large Discrete-time Non-symmetric Algebraic Riccati Equations

This paper presents a numerical algorithm for solving large-scale discrete-time non-symmetric algebraic Riccati equations (DTNAREs) that arise in game-theoretic computations of Nash equilibria. The proposed low-rank alternating direction implicit (ADI) method recursively constructs a low-rank stabilizing solution without explicitly solving large dense systems. The approach addresses computational prohibitive challenges in large-scale applications by exploiting the low-rank structure of the solution matrix.