总体最小二乘曲线曲面模型建立方法比较探究

Comparison of the Model of Curve and Surface by the Method of TLS

本文探究了总体最小二乘的3种方法,包括奇异值分解、最小奇异值方法和迭代法,并且对3种方法进行比较。在模型推导的基础上,文中对3种总体最小二乘法在曲线和曲面拟合中求解的参数及其精度进行了比较分析。通过与最小二乘法的比较表明:总体最小二乘法得到的拟合结果更加稳健,并且发现迭代法和奇异值分解方法的结果是一样的;最小奇异值方法的结果欠优。

The authors explore three methods of total least squares,including singular value decomposition,minimum singular value method and iteration method,and compare three methods. Also the author compared and analyzed the parameters and the accuracy of the 3 total least squares method in curve and surface fitting based on the deduction of the model. Through the examples’ results show that the total least squares method is used to get the fitting results more robust,and found that iterative method and singular value decomposition method,which the result is the same; the minimum singular value method result is not good compared with the two other methods.