矩阵最小二乘问题的迭代求解及其在机器翻译中的应用
王在华
摘要：本文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。
【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
Zaihua Wang
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.
Keywords:machine translation;least square problem;iteration;gradient matrix;gradient descent algorithm
原文链接：https://kns.cnki.net/KCMS/detail/detail.aspx?dbname=cjfd2021&filename=ssjs202107014&dbcode=cjfq
