首先，在這篇論文中，我們將簡單描述解奇異黎卡迪方程的二次根數值方法。接著我們將討論解奇異黎卡迪方程的對稱半正定解的保結構數值方法。近來，二次變換的保結構方法因為良好的數值行為而又重新受到重視，我們將在一些設定條件的例子中，比較保結構方法跟二次根的數值結果。

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

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