1、最小二乘法的应用研究最小二乘法的应用研究 摘摘 要要 最小二乘法是从误差拟合角度对回归模型进行参数估计或系统辨识,并在 参数估计、系统辨识以及预测、预报等众多领域中得到极为广泛的应用.然而, 最小二乘法因其抽象、难懂常常不能被准确理解.本文探讨了最小二乘法的基本 原理及其各种变形的拟合方法,其中包括:一元线性最小二乘法拟合、 多元线性拟 合、多项式拟合、非线性拟合,并且讨论了用镜像映射和切比雪夫多项式解“病 态”矛盾方程组的基本原理和方法,在此基础上给出了几种最小二乘法程序的设 计原理. 关键词关键词：最小二乘法,线性拟合,曲线拟合,切比雪夫多项式 Study on the Applicati
2、on about Method of Least Square Abstract Least square was used to estimate parameters and identify system of regression model, by the point of error fitting. And it has widely application in the parameters estimate, system identification, prediction, forecasting and other fields. However, the least
3、square method because of its abstract and difficult ，often can not be accurately understanding. The least square methods principle and the various kinds of fitting methods such as the linear least square fitting, multiple linear fitting, polynomial fitting a nonlinear fitting are dealt with. And dis
4、cussed using mirror and Chebyshev polynomial solution pathological contradictory equations basic principles and methods. Finally some kinds of the principle of the programs on the least square method are given. Key Words：least square method, linear fitting, curve fitting, Chebyshev polynomial 目目 录录
5、一、最小二乘法的统计学原理1 二、曲线拟合2 1.一元线性拟合2 2.多元线性拟合4 3.多项式拟合5 4.非线性最小二乘法拟合6 5.多项式回归的高精度快速算法7 三、应用最小二乘法的几个问题9 四、 程序设计原理10 1.线性拟合程序的设计原理10 2.多元线性拟合程序的设计原理10 3.Shehata 方程 12 12 k sk s u ksks 的拟合程序设计原理11 结束语11 参考文献12 1 一一、最小二乘法的统计学原理最小二乘法的统计学原理 1 基本最小二乘法,其统计学原理是: 设物理量y与l个变量 12 , l xxx间的依赖关系式为 1201 (,) ln yfxxxaaa, 其中 01 , n aaa是方程中需要确定的1n 个参数. 最小二乘法就是通过1mmn个实验点 12 (,)(1, 2,) iiili xxxyim ,确定 出一组参数值 01 (,) n aaa, 使由这组参数得出的函数值 1201 =(,) ii
