An iterative algorithm for solving a class of matrix equations

An iterative algorithm for solving a class of matrix equations

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摘要 In this paper, an iterative algorithm is presented to solve the Sylvester and Lyapunov matrix equations. By this iterative algorithm, for any initial matrix X1, a solution X＊ can be obtained within finite iteration steps in the absence of roundoff errors. Some examples illustrate that this algorithm is very efficient and better than that of [ 1 ] and [2]. In this paper, an iterative algorithm is presented to solve the Sylvester and Lyapunov matrix equations. By this iterative algorithm, for any initial matrix X1, a solution X＊ can be obtained within finite iteration steps in the absence of roundoff errors. Some examples illustrate that this algorithm is very efficient and better than that of [ 1 ] and [2].

作者 Minghui WANG Yan FENG

机构地区 School of Mathematical Sciences College of Information Science ＆ Technology

出处《控制理论与应用（英文版）》 EI 2009年第1期68-72,共5页

基金 supported by the National Natural Science Foundation of China (No.10771073)

关键词 Iterative algorithm Conjugate gradient method Lyapunov matrix equation Sylvester matrix equation Iterative algorithm Conjugate gradient method Lyapunov matrix equation Sylvester matrix equation

分类号 O231 [理学—运筹学与控制论] TP273 [自动化与计算机技术—检测技术与自动化装置]

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1Micka?l Robbé,Miloud Sadkane.A Convergence Analysis of Gmres and Fom Methods for Sylvester Equations[J].Numerical Algorithms.2002(1)
2A. El Guennouni,K. Jbilou,A.J. Riquet.Block Krylov Subspace Methods for Solving Large Sylvester Equations[J].Numerical Algorithms (-).2002(1-3)
3Peter Benner,Enrique S. Quintana-Ortí.Solving stable generalized Lyapunov equations with the matrix sign function[J].Numerical Algorithms.1999(1)
4Y.Peng.The Iterative Method for the Solutions and Optimal Approximation of the Constrained Matrix Equation[]..2004
5Ding F,Chen T.Gradient based iterative algorithms for solving a class of matrix equations[].IEEE Transactions on Automatic Control.2005
6Benner P.Quintanna-Orti E.S. Solving Stable Generalized Lyapunov Equations with the Matrix Sign Function[].Numerical Algorithms.1999
7Bitmead R.Explicit solutions of the discrete-time Lyapunov matrix equation and Kalman-Yakubovich equations[].IEEE Transactions on Automatic Control.1981
8Heinen J.A technique for solving the extended discrete Lyapunov matrix equation[].IEEE Transactions on Automatic Control.1972
9Bitmead R,Weiss H.On the solution of the discrete-time Lyapunov matrix equation in controllable canonical form[].IEEE Transactions on Automatic Control.1979
10Golub GH,Nash S,Van Loan CF.A Hessenberg-Schur method for the matrix problem AX + XB = C[].IEEE Transactions on Automatic Control.1979

1王才良,史泽林,李德强.图像重构中估计基础矩阵的线性迭代算法[J].微计算机信息,2006(03S):221-223. 被引量：2
2Li Wang,QingwenWang,Zhuoheng He.The Common Solution of Some Matrix Equations[J].Algebra Colloquium,2016,23(1):71-81. 被引量：2
3REHMAN Abdur,WANG Qingwen.Common least-squares solution to some matrix equations[J].上海大学学报（自然科学版）,2017,23(2):267-275.
4Yu-Peng Qiao,Hong-Sheng Qi,Dai-Zhan Cheng.Parameterized Solution to a Class of Sylvester Matrix Equations[J].International Journal of Automation and computing,2010,7(4):479-483.
5熊九龙,林存宝.基于实际物理距离的基本矩阵估计[J].电子测量与仪器学报,2009,23(11):19-24. 被引量：1
6吴红英.时空分数阶对流-弥散方程组的有限元方法[J].吉首大学学报（自然科学版）,2016,37(1):7-10.
7令狐昌仁.线性规划的一种线性算法(英文)[J].贵州科学,1997,15(4):264-271.
8Jun＇ e FENG,Peng CUI,Zhaolin CHENG.H-infinity output feedback control for descriptor systems with delayed states[J].控制理论与应用（英文版）,2005,3(4):341-347.
9Guangjing Song,Shaowen Yu,Ming Chen.A New Expression of the Hermitian Solutions to a System of Matrix Equations with Applications[J].Algebra Colloquium,2016,23(1):167-180.
10李范良,胡锡炎,张磊.THE GENERALIZED REFLEXIVE SOLUTION FOR A CLASS OF MATRIX EQUATIONS (AX-B,XC=D)[J].Acta Mathematica Scientia,2008,28(1):185-193. 被引量：7

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An iterative algorithm for solving a class of matrix equations

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