| 矩阵最小二乘问题的迭代求解及其在机器翻译中的应用 |
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| 引用本文： | 王在华.矩阵最小二乘问题的迭代求解及其在机器翻译中的应用[J].数学的实践与认识,2021(7):119-126. |
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| 作者姓名： | 王在华 |
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| 作者单位： | 陆军工程大学基础部基础数学教研室 |
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| 基金项目： | 国家自然科学基金面上项目(12072370)。 |
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| 摘 要： | 研究一类线性矩阵方程最小二乘问题的迭代法求解,利用目标函数与矩阵迹之间的关系构造了矩阵形式的"梯度"下降法迭代格式,推广了向量形式的经典"梯度"下降法,并引入了两个矩阵之间的弱正交性来刻画迭代修正量的特点.作为本文算法的应用,给出了机器翻译优化问题的一种迭代求解格式.
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| 关 键 词： | 机器翻译 最小二乘问题 迭代 梯度矩阵 梯度下降法 |
A Matrix Iterative Algorithm for a Least Square Problem with Application to Machine Translation |
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| WANG Zai-hua.A Matrix Iterative Algorithm for a Least Square Problem with Application to Machine Translation[J].Mathematics in Practice and Theory,2021(7):119-126. |
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| Authors: | WANG Zai-hua |
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| Institution: | (Department of Basic Courses,Army Engineering University,Nanjing 211101,China) |
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| Abstract: | This paper investigates the numerical solution to the least square problem of a class of linear matrix equations.Based on the relationship between the objective function and trace of matrix,a gradient descent algorithm in matrix iteration form is proposed,strong orthogonality and weak orthogonality of two matrices are introduced.As a direct generalization of the classical gradient descent algorithm for least square problem in vector iteration form,the proposed algorithm is applied to solve the least square problem arising from machine translation. |
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| Keywords: | machine translation least square problem iteration gradient matrix gradient descent algorithm |
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