On the solution of large-scale algebraic Riccati equations by using low-dimensional invariant subspaces
On the solution of large-scale algebraic Riccati equations by using low-dimensional invariant subspaces
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DOI：
10.1016/j.laa.2015.09.027
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发表时间：
2016-01-01
影响因子：
1.1
通讯作者：
Bujanovic, Zvonimir
中科院分区：
文献类型：
--
作者：
Benner, Peter;Bujanovic, Zvonimir
讨论了一种通过计算Hamilton矩阵的低维稳定不变子空间来求解大型代数Riccati方程的方法。我们给战神接纳低数值秩的解决方案的条件，并表明这些可以近似通过哈密顿特征空间。我们讨论的战略选择适当的特征空间，产生一个良好的近似，和不同的公式建立近似本身。我们的方法与其他几种方法解决战神的相似之处示出：密切相关的是projectiontype的方法，使用各种Krylov子空间和qADI算法。本文的目的仅仅是分析计算近似Riccati解决方案的可能性，从低维子空间相关的相应的哈密顿矩阵，并解释现有的方法之间的共性，而不是提供一个新的算法。(C)2015 Elsevier Inc. All rights reserved.
This article discusses an approach to solving large-scale algebraic Riccati equations (AREs) by computing a lowdimensional stable invariant subspace of the associated Hamiltonian matrix. We give conditions on AREs to admit solutions of low numerical rank and show that these can be approximated via Hamiltonian eigenspaces. We discuss strategies on choosing the proper eigenspace that yields a good approximation, and different formulas for building the approximation itself. Similarities of our approach with several other methods for solving AREs are shown: closely related are the projectiontype methods that use various Krylov subspaces and the qADI algorithm. The aim of this paper is merely to analyze the possibilities of computing approximate Riccati solutions from low-dimensional subspaces related to the corresponding Hamiltonian matrix and to explain commonalities among existing methods rather than providing a new algorithm. (C) 2015 Elsevier Inc. All rights reserved.