鲁铁定, 陶本藻, 周世健. 基于整体最小二乘法的线性回归建模和解法[J]. 武汉大学学报 ( 信息科学版), 2008, 33(5): 504-507.
引用本文: 鲁铁定, 陶本藻, 周世健. 基于整体最小二乘法的线性回归建模和解法[J]. 武汉大学学报 ( 信息科学版), 2008, 33(5): 504-507.
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LU Tieding, TAO Benzao, ZHOU Shijian. Modeling and Algorithm of Linear Regression Based on Total Least Squares[J]. Geomatics and Information Science of Wuhan University, 2008, 33(5): 504-507.
Citation: LU Tieding, TAO Benzao, ZHOU Shijian. Modeling and Algorithm of Linear Regression Based on Total Least Squares[J]. Geomatics and Information Science of Wuhan University, 2008, 33(5): 504-507.
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基于整体最小二乘法的线性回归建模和解法

Modeling and Algorithm of Linear Regression Based on Total Least Squares

    摘要
  • 摘要: 对基于自变量和因变量误差的回归问题进行了进一步研究,证明了两种方法的实质并未解决同时考虑自变量和因变量的误差问题,其解算结果和不考虑自变量误差的解算结果完全相同。给出了能同时顾及自变量和因变量误差的新的回归模型,并推导了具体的解算方法。算例结果和基于矩阵分解的整体最小二乘法解算方法的结果相同,说明了本文方法的正确性。

     

    Abstract: The independent variables error and variables error are further studied.A new regression model is given,and calculation algorithms are deduced.Numerical experiments are used to demonstrate correctness of the new method,and the results are same as those of the total least square method.The algorithms proposed in this paper simplify the complicated matrix decomposing calculation,bring TLS into category of surveying adjustment.

     

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