| 矩阵方程组异类约束解的MCG1-3-5算法 |
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| 引用本文： | 陈世军.矩阵方程组异类约束解的MCG1-3-5算法[J].福建工程学院学报,2018,0(4):365-371. |
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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： | 借鉴求线性矩阵方程组同类约束解的MCG算法（修正共轭梯度法），建立了求多个未知矩阵的线性矩阵方程组的一种异类约束解的MCG1-3-5算法，证明了该算法的收敛性。该算法不仅可以判断矩阵方程组的异类约束解是否存在，而且在有异类约束解，且不考虑舍入误差时，可在有限步计算后求得矩阵方程组的一组异类约束解；选取特殊初始矩阵时，求得矩阵方程组的极小范数异类约束解。同时还能求取指定矩阵在该矩阵方程组异类约束解集合中的最佳逼近。算例表明，该算法有效。
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| 关 键 词： | 线性矩阵方程组 异类约束矩阵 MCG1-3-5算法 收敛性 最佳逼近 |
An MCG1-3-5 algorithm for heterogeneous constrained solutions of matrix equations |
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| CHEN Shijun.An MCG1-3-5 algorithm for heterogeneous constrained solutions of matrix equations[J].Journal of Fujian University of Technology,2018,0(4):365-371. |
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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: | Based on the modified conjugate gradient method (MCG) for the same constrained solutions of linear matrix equations, a modified conjugate method MCG1-3-5 was established for heterogeneous constrained solutions of linear matrix equations with multiple unknown matrices. The convergence of this algorithm was also proved. This algorithm can not only judge the existence of heterogeneous constrained solutions of matrix equations, but also obtain a set of such solutions within finite iterative steps in the absence of round off errors when there do exist heterogeneous constrained solutions. When a special initial matrix is selected, the heterogeneous constrained solution with a minimal norm can be obtained for the matrix equations. Meanwhile, the optimal approximation of the given matrix can be obtained in the set of the above-mentioned solutions. The example shows that the method is quite effective. |
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| Keywords: | linear matrix equations heterogeneous constrained matrices modified conjugate gradient method 1-3-5(MCG1-3-5) convergence optimal approximation |
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