| 非线性矩阵方程双对称解的牛顿-MCG算法 |
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| 引用本文： | 陈世军.非线性矩阵方程双对称解的牛顿-MCG算法[J].福建工程学院学报,2019,0(3):302-306. |
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| 作者姓名： | 陈世军 |
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| 作者单位： | 福建工程学院应用技术学院 |
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| 摘 要： | 研究一类含有三次逆幂非线性矩阵方程双对称解数值计算问题。先用牛顿算法迭代计算导出线性矩阵方程双对称解，再用修正共轭梯度算法(MCG算法)求由牛顿算法导出的线性矩阵方程双对称解或最小二乘双对称解。建立牛顿MCG算法求这类矩阵方程双对称解，数值算例表明牛顿-MCG算法是有效的。
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| 关 键 词： | 含三次逆幂的非线性矩阵方程 双对称解 修正共轭梯度法 |
A Newton-MCG algorithm for bisymmetric solutions of nonlinear matrix equation |
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| CHEN Shijun.A Newton-MCG algorithm for bisymmetric solutions of nonlinear matrix equation[J].Journal of Fujian University of Technology,2019,0(3):302-306. |
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| Authors: | CHEN Shijun |
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| Institution: | School of Applied Technology, Fujian University of Technology |
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| Abstract: | The numerical calculation of bisymmetric solutions was conducted for a class of nonlinear matrix equation with cubic inverse power. The bisymmetric solution of the linear matrix equation was obtained by iterative calculation with the Newton algorithm. Then the bisymmetric matrix solution or minimum square bisymmetric matrix solution of the linear matrix equation derived from the Newton algorithm is obtained by the modified conjugate gradient algorithm(MCG algorithm). Numerical examples show that the Newton-MCG algorithm is effective. |
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| Keywords: | cubic inverse-power nonlinear matrix equations bisymmetric solutions modified conjugate gradient method |
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