Generalized conjugate direction algorithm for solving general coupled Sylvester matrix equations
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DOI码：10.1016/j.jfranklin.2023.08.022
发表刊物：Journal of the Franklin Institute
关键字：General coupled Sylvester matrix equations, generalized conjugate direction algorithm, least squares solution, inner product space
摘要：In this paper, a generalized conjugate direction algorithm (GCD) is proposed for solving general coupled Sylvester matrix equations. The GCD algorithm is an improved gradient algorithm, which can realize gradient descent by introducing matrices $P_{j}(k)$ and $T_{j}(k)$ to construct parameters $\alpha(k)$ and $\beta(k)$. The matrix $P_{j}(k)$ and $T_{j}(k)$ are iterated in a cross way to accelerate the convergence rate. In addition, it is further proved that the algorithm converges to the exact solution in finite iteration steps in the absence of round-off errors if the system is consistent. Also, the sufficient conditions for least squares solutions and the minimum F-norm solutions are obtained. Finally, numerical examples are given to demonstrate the effectiveness of the GCD algorithm.
第一作者：Zijian Zhang
论文类型：期刊论文
通讯作者：Xuesong Chen
卷号：360
期号：14
页面范围：10409-10432
是否译文：否
发表时间：2023-09-05
收录刊物：SCI
发布期刊链接：https://doi.org/10.1016/j.jfranklin.2023.08.022
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