目录TOC\o"1-3"\h\z\uHYPERLINK\l"_Toc294458058"摘要PAGEREF_Toc294458058\h3HYPERLINK\l"_Toc294458059"ABSTRACTPAGEREF_Toc294458059\h4HYPERLINK\l"_Toc294458060"第一章引言PAGEREF_Toc294458060\h5HYPERLINK\l"_Toc294458061"第二章最小二乘法PAGEREF_Toc294458061\h5HYPERLINK\l"_Toc294458062"2.1最小二乘拟合PAGEREF_Toc294458062\h5HYPERLINK\l"_Toc294458063"2.2线性最小二乘拟合PAGEREF_Toc294458063\h6HYPERLINK\l"_Toc294458064"2.3小结PAGEREF_Toc294458064\h7HYPERLINK\l"_Toc294458065"第三章快速算法及基本原理PAGEREF_Toc294458065\h7HYPERLINK\l"_Toc294458066"3.1H-变换PAGEREF_Toc294458066\h7HYPERLINK\l"_Toc294458067"3.2QR分解PAGEREF_Toc294458067\h10HYPERLINK\l"_Toc294458068"3.3算法PAGEREF_Toc294458068\h11HYPERLINK\l"_Toc294458069"第四章最小二乘法的正交化方法PAGEREF_Toc294458069\h13HYPERLINK\l"_Toc294458070"第五章matlab代码实现PAGEREF_Toc294458070\h14HYPERLINK\l"_Toc294458071"5.1Householder变换PAGEREF_Toc294458071\h14HYPERLINK\l"_Toc294458072"5.2用householder变换来做QR分解PAGEREF_Toc294458072\h15HYPERLINK\l"_Toc294458073"5.3QR分解PAGEREF_Toc294458073\h16HYPERLINK\l"_Toc294458074"第六章应用PAGEREF_Toc294458074\h17HYPERLINK\l"_Toc294458075"第七章总结PAGEREF_Toc294458075\h18HYPERLINK\l"_Toc294458076"谢辞PAGEREF_Toc294458076\h19HYPERLINK\l"_Toc294458077"参考文献PAGEREF_Toc294458077\h20HYPERLINK\l"_Toc294458078"注释PAGEREF_Toc294458078\h21HYPERLINK\l"_Toc294458079"附录PAGEREF_Toc294458079\h22摘要本文介绍了数据拟合中最小二乘法的基本原理，并根据最小二乘数据拟合方法，针对线性最小二乘拟合及其快速算法（运用HOUSEHOLDER变换及QR分解）进行了分析和研究，并通过数学工具Matlab实现了对相关问题的举例应用，使相关数据拟合理论更加生动易懂.关键词：数据拟合，最小二乘法，householder变换，应用ABSTRACTThisthesisintroducesthebasicprincipleoftheleastsquaredatafitting.Accordingtotheleastsquaredatafitting,thepaperstudiesandanalyzesthelinearleastsquarefittingusingtheHouseholdermatrixtransformationsandQRdecompositionsofthematrix.UsingMatlabmakesthetheoryofdatafittingeasiertobeunderstood.ThemethodofoperationandcomposeofMatlabisquiteeasyandtheresultisaccurate.