Global extended Krylov subspace methods for large-scale differential Sylvester matrix equations
Global extended Krylov subspace methods for large-scale differential Sylvester matrix equations
复制标题
大规模微分 Sylvester 矩阵方程的全局扩展 Krylov 子空间方法
DOI：
10.1007/s12190-019-01278-7
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
H. Alaoui
中科院分区：
文献类型：
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作者：
E. Sadek;A. Bentbib;L. Sadek;H. Alaoui
本文给出了求解具有低秩右侧的大规模Sylvester矩阵微分方程的一种新的数值方法。这些微分矩阵方程出现在许多应用中，如鲁棒控制问题、模型约简问题等。我们提出了两种基于扩展全局Arnoldi过程的方法。第一种方法是利用全局扩展Krylov方法逼近精确解中的指数矩阵。第二种方法是利用扩展的全局Arnoldi算法对相应的Sylvester方程的解进行低秩逼近。我们给出了一些理论结果，并报告了一些数值实验，以证明所提出的方法与Hached和Jbilou给出的扩展块Krylov方法（数字线性代数应用255:e2187, 2018）的有效性。
In this paper, we present a new numerical methods for solving large-scale differential Sylvester matrix equations with low rank right hand sides. These differential matrix equations appear in many applications such as robust control problems, model reduction problems and others. We present two approaches based on extended global Arnoldi process. The first one is based on approximating exponential matrix in the exact solution using the global extended Krylov method. The second one is based on a low-rank approximation of the solution of the corresponding Sylvester equation using the extended global Arnoldi algorithm. We give some theoretical results and report some numerical experiments to show the effectiveness of the proposed methods compared with the extended block Krylov method given in Hached and Jbilou (Numer Linear Algebra Appl 255:e2187, 2018).