The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati Equation
We use a second-order learning algorithm for numerically solving a class of the algebraic Riccati equations. Specifically, the extended Hamiltonian algorithm based on manifold of positive definite symmetric matrices is provided. Furthermore, this algorithm is compared with the Euclidean gradient alg...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/693659 |
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| _version_ | 1832565667032727552 |
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| author | Zhikun Luo Huafei Sun Xiaomin Duan |
| author_facet | Zhikun Luo Huafei Sun Xiaomin Duan |
| author_sort | Zhikun Luo |
| collection | DOAJ |
| description | We use a second-order learning algorithm for numerically solving a class
of the algebraic Riccati equations. Specifically, the extended Hamiltonian algorithm based on manifold
of positive definite symmetric matrices is provided. Furthermore, this algorithm is compared with the
Euclidean gradient algorithm, the Riemannian gradient algorithm, and the new subspace iteration method.
Simulation examples show that the convergence speed of the extended Hamiltonian algorithm is the
fastest one among these algorithms. |
| format | Article |
| id | doaj-art-afe6da2704a344e0a128ea775de09bb0 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-afe6da2704a344e0a128ea775de09bb02025-02-03T01:07:01ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/693659693659The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati EquationZhikun Luo0Huafei Sun1Xiaomin Duan2School of Mathematics, Beijing Institute of Technology, Beijing 100081, ChinaSchool of Mathematics, Beijing Institute of Technology, Beijing 100081, ChinaSchool of Mathematics, Beijing Institute of Technology, Beijing 100081, ChinaWe use a second-order learning algorithm for numerically solving a class of the algebraic Riccati equations. Specifically, the extended Hamiltonian algorithm based on manifold of positive definite symmetric matrices is provided. Furthermore, this algorithm is compared with the Euclidean gradient algorithm, the Riemannian gradient algorithm, and the new subspace iteration method. Simulation examples show that the convergence speed of the extended Hamiltonian algorithm is the fastest one among these algorithms.http://dx.doi.org/10.1155/2014/693659 |
| spellingShingle | Zhikun Luo Huafei Sun Xiaomin Duan The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati Equation Journal of Applied Mathematics |
| title | The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati Equation |
| title_full | The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati Equation |
| title_fullStr | The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati Equation |
| title_full_unstemmed | The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati Equation |
| title_short | The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati Equation |
| title_sort | extended hamiltonian algorithm for the solution of the algebraic riccati equation |
| url | http://dx.doi.org/10.1155/2014/693659 |
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