Some matrix equations are important in application and studying in various fields of sciences. One of them is continuous-time algebraic Riccati matrix equation that is an interesting subject for many researchers in engineering and sciences specially applied mathematics. In this work we try to apply Hermitian and skew-Hermitian splitting (HSS) like method to solve this equation. Then we analyze the convergence of the new iterative method in detail. Also we try to determine the optimum parameter in our method which minimizes the upper bounds of absolute error. In the end we test the new algorithm by solving some numerical examples.

一些矩阵方程在各个科学领域的应用和研究中都很重要。其中之一是连续时间代数 Riccati 矩阵方程，这是许多工程和科学特别是应用数学研究人员感兴趣的课题。在这项工作中，我们尝试应用 Hermitian 和 skew-Hermitian splitting (HSS) 之类的方法来求解该方程。然后我们详细分析了新迭代方法的收敛性。我们还尝试确定我们方法中的最佳参数，以最小化绝对误差的上限。最后，我们通过求解一些数值例子来测试新算法。