在我们的实验中经常遇到的就是数据拟合成曲线的问题，而Matlab在这方面具有极为强大的功能。

今天特开一帖，希望大家总结一下经常遇到的拟合情况，版主将予以不同程度的奖励，望大家踊跃发言！


回帖格式：

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【拟合　目标】：
【函数｜方法】：
【具体　实例】：

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来个最简单的：

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【拟合　目标】：多项式
【函数｜方法】：polyfit,polyval
【具体　实例】：

x=0:0.1:5;
y=exp(-5*x)+x.*x;
subplot(2,1,1),plot(x,y,'r+'),hold on
p=polyfit(x,y,2)
yp=polyval(p,x);
plot(x,yp,'bo')
subplot(2,1,2),plot(yp-y,'*')

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奖励
　　尘埃122

金币　：10
经验　：10
魅力　：10
金钱　：20

ydgsl是这方面的大牛，给大家系统说说非线性拟合的情况啊

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【拟合　目标】：多元线性拟合y=a1*x1+a2*x2+..+am*xm
【函数｜方法】：pinv,\

【具体　实例】：数据点{x1i,x2i,…xmi,yi}，

A=|x12,x22,…xm2|
|…………… |
|x1n,x2n,…xmn|

Y={y1,y2,y3,…,yn}'

则系数{a1,a2,…,am}'=pinv(A)*Y
在matlab中使用
coeff=A\Y
则可以得到最小二乘意义上的拟合系数

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【转】Matlab中如何作圆回归
:#Peter Boettcher (boettcher@ll.mit.edu),2002/5/16, comp.soft-sys.matlab#

Q5.5: How can I fit a circle to a set of XY data?
=================================================

An elegant chunk of code to perform least-squares circle fitting was
written by Bucher Izhak and has been floating around the newgroup for
some time. The first reference to it that I can find is in:

function [xc,yc,R,a] = circfit(x,y)
%CIRCFIT Fits a circle in x,y plane
%
% [XC, YC, R, A] = CIRCFIT(X,Y)
% Result is center point (yc,xc) and radius R.A is an optional
% output describing the circle's equation:
%
% x^2+y^2+a(1)*x+a(2)*y+a(3)=0

% by Bucher izhak 25/oct/1991

n=length(x); xx=x.*x; yy=y.*y; xy=x.*y;
A=[sum(x) sum(y) n;sum(xy) sum(yy) sum(y);sum(xx) sum(xy) sum(x)];
B=[-sum(xx+yy) ; -sum(xx.*y+yy.*y) ; -sum(xx.*x+xy.*y)];
a=A\B;
xc = -.5*a(1);
yc = -.5*a(2);
R = sqrt((a(1)^2+a(2)^2)/4-a(3));

Tom Davis provided a more sophisticated approach that works for more
cases in and Code included.