单变量矩阵方程子矩阵约束下牛顿-MCG算法  

NEWTON MCG ALGORITHM WITH SUBMATRIX CONSTRAINTS FOR UNIVARIATE MATRIX EQUATION

作　　者：陈世军 卢民荣[2] Chen Shijun;Lu Mingrong(Fujian university of technology college of Applied Technology,Fuzhou 350001,China;School of Accountancy of Fujian JiangXia university,Fuzhou 350001,China)

机构地区：[1]福建工程学院应用技术学院,福州350001 [2]福建江夏学院会计学院,福州350001

出　　处：《数值计算与计算机应用》2020年第4期306-314,共9页Journal on Numerical Methods and Computer Applications

基　　金：2019年福建省教育厅中青年教育科研项目(JAT190410);2018年福建省教育厅中青年教育科研项目(JZ180190)资助.

摘　　要：子矩阵约束问题源于实际应用中的子系统扩张问题,文中研究了子矩阵约束下二次矩阵方程对称解的迭代算法,先用牛顿算法把二次矩阵方程转化为关于校正矩阵的线性矩阵方程,再用修正共轭梯度算法(MCG算法)求解导出线性矩阵方程对称解或最小二乘解,建立了求单变量二次矩阵方程子矩阵约束下对称解牛顿-MCG算法.数值算例表明,该牛顿-MCG是有效的,能在有限步迭代得到方程的子矩阵约束解.The problem of submatrix constraint originates from the problem of subsystem expansion in practical application.This paper studies the iterative algorithm of the symmetric solution of the quadratic matrix equation under Submatrix Constraint.First,the quadratic matrix equation is transformed into the linear matrix equation about the correction matrix by Newton algorithm,and then the symmetric solution or the least square solution of the linear matrix equation is derived by the modified conjugate gradient algorithm(MCG algorithm)The Newton-MCG algorithm for solving symmetric solution of quadratic matrix equation with single variable is presented.Numerical examples show that the Newton MCG is effective and can obtain the submatrix constrained solution of the equation in finite steps.

关 键 词：牛顿算法 对称解 修正共轭梯度法 子矩阵约束解 最小二乘解 

分 类 号：O241.6[理学—计算数学]