| 双变量矩阵方程组对称最小二乘解的迭代算法 |
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| 引用本文： | 郑凤芹,张凯院,武见. 双变量矩阵方程组对称最小二乘解的迭代算法[J]. 数学杂志, 2011, 31(6): 1117-1124 |
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| 作者姓名： | 郑凤芹 张凯院 武见 |
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| 作者单位： | 西北工业大学应用数学系,陕西西安,710072 |
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| 摘 要： | 本文研究了求双变量线性矩阵方程组的对称最小二乘解的问题.利用求解线性代数方程组的共轭梯度法的基本思想,通过对有关矩阵和系数的变形与近似处理,建立了一种迭代算法.拓宽了共轭梯度法的适用范围.算例表明,迭代算法是有效的.
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| 关 键 词： | 线性矩阵方程组 对称最小二乘解 极小范数最小二乘解 迭代算法 最佳逼近 |
AN ITERATIVE METHOD FOR THE LEAST-SQUARES SYMMETRIC SOLUTIONS OF THE MATRIX EQUATIONS WITH DOUBLE-VARIABLE |
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| ZHENG Feng-qin,ZHANG Kai-yuan,WU Jian. AN ITERATIVE METHOD FOR THE LEAST-SQUARES SYMMETRIC SOLUTIONS OF THE MATRIX EQUATIONS WITH DOUBLE-VARIABLE[J]. Journal of Mathematics, 2011, 31(6): 1117-1124 |
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| Authors: | ZHENG Feng-qin ZHANG Kai-yuan WU Jian |
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| Affiliation: | ZHENG Feng-qin,ZHANG Kai-yuan,WU Jian (Dept.of Applied Mathematics,Northwestern Polytechnical University,Xi'an 710072,China) |
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| Abstract: | The article studies the problem of the least-squares symmetric solutions of the linear matrix equations with double-variable.We use the conjugate gradient method for solving linear algebraic equations and the special transformation and approximate disposal for the relative matrices and coefficient.Expand the application of the conjugate gradient method,numerical experiments show that the iterative algorithm is quite efficient. |
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| Keywords: | linear matrix equations the least-squares symmetric solutions least-squares solutions with least-norm iterative method optimal approximation |
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