一类过阻尼系统二次方程的快速迭代算法  

A Quick Iterative Algorithm for Quadratic Equations in an Overdamped System

作　　者：金继承[1] 董宁[1] 蔡汝忠 JIN Jicheng;DONG Ning;CAI Ruzhong(College of Science,Hunan University of Technology,Zhuzhou Hunan 412007,China)

机构地区：[1]湖南工业大学理学院,湖南株洲412007

出　　处：《湖南工业大学学报》2018年第1期1-5,15,共6页Journal of Hunan University of Technology

基　　金：湖南省自然科学基金资助项目(2017JJ2071);湖南省教育厅优秀青年基金资助项目(17B071);湖南省教育厅基金资助项目(17C0466)

摘　　要：考虑一类来自过阻尼系统的二次矩阵方程数值求解问题,针对方程系数矩阵的结构特点,设计了一种快速求解方程的迭代算法,给出了这类算法具体的迭代格式和收敛性。数值实验表明,提出的算法能够有效地求解此类方程具有实际意义的解。Aiming at the numerical solution of quadratic matrix equations in an overdamped system,and based on an analysis of the structural properties of the coefficient matrix of the equation,an iterative algorithm for a quick solution of the equation has thus been proposed,with its specific iterative format and convergence subsequently given.The numerical experiments show that the proposed algorithm is of practical significance for the effective solution of this kind of equation.

关 键 词：过阻尼系统 二次方程 保结构加倍算法 TOEPLITZ矩阵 HANKEL矩阵 

分 类 号：O151.21[理学—数学] TP273[理学—基础数学]