Solution of Algebraic Lyapunov Equation on Positive-Definite Hermitian Matrices by Using Extended Hamiltonian Algorithm
作者机构：Department of MathematicsAir UniversityPAF ComplexE-9IslamabadPakistan Department of MathematicsComsats Institute of Information TechnologyPark RoadChak-ShahzadIslamabadPakistan Department of MathematicsComsats Institute of Information TechnologyWah CanttPakistan
出 版 物：《Computers, Materials & Continua》 (计算机、材料和连续体（英文）)
年 卷 期：2018年第54卷第2期
页 面：181-195页
核心收录：
学科分类：0831[工学-生物医学工程（可授工学、理学、医学学位）] 0808[工学-电气工程] 07[理学] 0809[工学-电子科学与技术（可授工学、理学学位）] 0805[工学-材料科学与工程（可授工学、理学学位）] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 0812[工学-计算机科学与技术（可授工学、理学学位）]
主 题：Information geometry algebraic lyapunov equation positive-definite hermitianmatrix manifold natural gradient algorithm extended hamiltonian algorithm
摘 要：This communique is opted to study the approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices.We choose the geodesic distance betweenAHXXA and P as the cost function,and put forward the Extended Hamiltonian algorithm(EHA)and Natural gradient algorithm(NGA)for the solution.Finally,several numerical experiments give you an idea about the effectiveness of the proposed algorithms.We also show the comparison between these two algorithms EHA and NGA.Obtained results are provided and analyzed graphically.We also conclude that the extended Hamiltonian algorithm has better convergence speed than the natural gradient algorithm,whereas the trajectory of the solution matrix is optimal in case of Natural gradient algorithm(NGA)as compared to Extended Hamiltonian Algorithm(EHA).The aim of this paper is to show that the Extended Hamiltonian algorithm(EHA)has superior convergence properties as compared to Natural gradient algorithm(NGA).Upto the best of author’s knowledge,no approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices is found so far in the literature.
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