Abstract
First of all, we summarize the square-root algorithm (SQR) for singular discretetimeRiccati difference equation (DRDE). And we will discuss the structure-preservingdoubling algorithms (SDAs) for the symmetric positive semidefinite solution tosingular version of the discrete-time algebraic Riccati equation (DARE). Recently,doubling algorithms have been revived for DARE because of their nice numericalbehavior, and we will compare the numerical behavior of SDA algorithm with SQRin some examples.