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Solution of large scale algebraic matrix riccati equations by use of hierarchical matrices
In previous papers, a class of hierarchical matrices ([Hamiltonian (script capital 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 [Hamiltonian (script capital H)]-matrix str...
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Published in: | Computing 2003-04, Vol.70 (2), p.121-165 |
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Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that cite this one |
Online Access: | Get full text |
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Summary: | In previous papers, a class of hierarchical matrices ([Hamiltonian (script capital 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 [Hamiltonian (script capital 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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ISSN: | 0010-485X 1436-5057 |
DOI: | 10.1007/s00607-002-1470-0 |