Low-Rank Cholesky Factor Krylov Subspace Methods for Generalized Projected Lyapunov Equations
Low-Rank Cholesky Factor Krylov Subspace Methods for Generalized Projected Lyapunov Equations
复制标题
广义投影 Lyapunov 方程的低阶 Cholesky 因子 Krylov 子空间方法
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
André K. Eppler
中科院分区：
文献类型：
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作者：
M. Bollhöfer;André K. Eppler
大规模的电路仿真产生的广义系统往往需要模型简化技术。在众多的降阶方法中，平衡截断法是一种常用的降阶模型构造方法。平衡截断方法的核心是求解一系列投影广义李雅普诺夫方程。在这篇文章中，我们提出了一个一般的框架，投影广义李雅普诺夫方程的数值解使用预处理Krylov子空间方法的基础上迭代与低秩Cholesky因子表示。这种方法可以被看作是替代LRCF-ADI方法，一个完善的方法求解李雅普诺夫方程。我们将证明，许多著名的Krylov子空间方法，如（F）GMRES，QMR，BICGSTAB和CG可以很容易地修改，以揭示底层的低秩结构。
Large-scale descriptor systems arising from circuit simulation often require model reduction techniques. Among many methods, Balanced Truncation is a popular method for constructing a reduced order model. In the heart of Balanced Truncation methods, a sequence of projected generalized Lyapunov equations has to be solved. In this article we present a general framework for the numerical solution of projected generalized Lyapunov equations using preconditioned Krylov subspace methods based on iterates with a low-rank Cholesky factor representation. This approach can be viewed as alternative to the LRCF-ADI method, a well established method for solving Lyapunov equations. We will show that many well-known Krylov subspace methods such as (F)GMRES, QMR, BICGSTAB and CG can be easily modified to reveal the underlying low-rank structures.