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The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati Equation

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  • Zhikun Luo
  • Huafei Sun
  • Xiaomin Duan

Abstract

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.

Suggested Citation

  • Zhikun Luo & Huafei Sun & Xiaomin Duan, 2014. "The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati Equation," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, May.
    • Handle: RePEc:hin:jnljam:693659
    DOI: 10.1155/2014/693659
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