| 子空间约束下矩阵方程ATXB+BTXTA=D的解及最佳逼近 |
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| 引用本文： | 冯艳昭,张澜.子空间约束下矩阵方程ATXB+BTXTA=D的解及最佳逼近[J].计算数学,2020,42(2):246-256. |
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| 作者姓名： | 冯艳昭 张澜 |
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| 作者单位： | 内蒙古工业大学理学院, 呼和浩特 010051 |
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| 摘 要： | 约束矩阵方程求解是指在满足一定约束条件下求矩阵方程（组）的解.在子空间约束条件下，利用共轭梯度法，结合线性投影算子，得到矩阵方程ATXB+BTXTA=D的解，进一步得到其最佳逼近.最后用数值例子证实了算法的有效性.
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| 关 键 词： | 子空间约束 共轭梯度 投影算子 最佳逼近 |
| 收稿时间： | 2018-11-30 |
THE SOLUTION AND OPTIMAL APPROXIMATION OF MATRIX EQUATION ATXB+BTXTA=D UNDER SUBSPACE CONSTRAINT |
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| Feng Yanzhao,Zhang Lan.THE SOLUTION AND OPTIMAL APPROXIMATION OF MATRIX EQUATION ATXB+BTXTA=D UNDER SUBSPACE CONSTRAINT[J].Mathematica Numerica Sinica,2020,42(2):246-256. |
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| Authors: | Feng Yanzhao Zhang Lan |
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| Institution: | Science of College, Inner Mongolia University of Technology, Hohhot 010051, China |
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| Abstract: | Solving the constrained matrix equation problem refers to finding the solution of the matrix equation (group) under certain constraint conditions. Under the constraint of subspace, by conjugate gradient method and linear projection operator, the solution of matrix equation ATXB+BTXTA=D and its optimal approximation are obtained. Finally, numerical examples are further used to verify the effectiveness of the algorithm. |
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| Keywords: | Subspace constraints Conjugate gradient Projection operator Optimal approximation |
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