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Solution of Large Scale Algebraic Matrix Riccati Equations by Use of Hierarchical Matrices
被引：0
作者：
L. Grasedyck
W. Hackbusch
B. N. Khoromskij
机构：
[1] Max-Planck-Institute for Mathematics in the Sciences Inselstr. 22–26 D-04103 Leipzig Germany e-mails: {lgr,
[2] wh,undefined
[3] bokh}@mis.mpg.de,undefined
来源：
Computing
|
2003年
/
70卷
关键词：
AMS Subject Classifications: 65F05, 65F30, 65F50.;
Keywords: Hierarchical matrices, data-sparse approximations, formatted matrix operations, fast solvers, Lyapunov equations, Riccati equations, control problems.;
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学科分类号：
摘要：
In previous papers, a class of hierarchical matrices (ℋ-matrices) is introduced which are data-sparse and allow an approximate matrix arithmetic of almost optimal complexity. Here, we investigate a new approach to exploit the ℋ-matrix structure for the solution of large scale Lyapunov and Riccati equations as they typically arise for optimal control problems where the constraint is a partial differential equation of elliptic type. This approach leads to an algorithm of linear-logarithmic complexity in the size of the matrices.
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页码：121 / 165
页数：44
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