The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati Equation. (20th May 2014)

• Record Type: Journal Article
• Authors: Luo, Zhikun; Sun, Huafei; Duan, Xiaomin
• Other Names: Shahzad Naseer Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2014(2014)
• Publication Date: 2014-05-20
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2014/693659
• Languages: English
• ISSNs: 1110-757X

Abstract

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.