Iterative algorithms based on weight splitting to solve Riccati matrix equation \(XDX-XC-BX+A=0\)

Algebraic Riccati matrix equations arise naturally in various situations and their role and application in systems, filtering, stochastic process, and control theory, in particular, have been well established in recent years. This study presents iterative algorithms to solve the algebraic Riccati matrix equation (ARME) \(\begin{aligned} R(X)=XDX-XC-BX+A=0, \end{aligned}\) $$\begin{array}{c}\hfill R(X)=XDX-XC-BX+A=0,\end{array}$$ based on the weight splitting (WS). We demonstrate that the iterative algorithms converge to non-positive and non-negative solutions of the ARME in special situations. To compare the new algorithms with the previously existing algorithm, we present some numerical examples.