[讨论]用matlab对一组数据拟合

liwenhui 发表于 2008-2-11 13:08

在本论坛乱逛，无意间发现一道题目，对初学matlab拟合者或许有参考意义。原题如下：<a href="http://www.madio.net/bbs/dispbbs.asp?boardID=110&ID=8603&page=17">http://www.madio.net/bbs/dispbbs.asp?boardID=110&ID=8603&page=17</a>我们现在来做其中的第一道拟合的题。题目重述如下：用表所给数据做2次和3次多项式拟合。试结合多项式拟合曲线对所得结果进行比较分析 
 
拟合数据 
 
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PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 53.25pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt;">56</td><td valign="top" width="71" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 53.25pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt;">116</td><td valign="top" width="71" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 53.25pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt;">206</td><td valign="top" width="71" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 53.25pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt;">332</td><td valign="top" width="71" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 53.3pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt;">500</td><td valign="top" width="71" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 53.3pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt;">716</td></tr></tbody></table> 
我们需要观察数据的变化趋势，用matlab画出散点图来。先对数据进行处理得到:x=-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 y=-1324 -994 -724 -508 -340 -214 -124 -64 -28 -10 -4 -4 -4 2 20 56 116 206 332 500 716绘制散点图。程序如下：clear allx=[-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10]; y=[-1324 -994 -724 -508 -340 -214 -124 -64 -28 -10 -4 -4 -4 2 20 56 116 206 332 500 716]; plot(x,y,'+')运行后得到的图像： 
可见，图像的变化趋势是一个比较理想的3次函数图像。对此，我们用3次函数进行拟合。程序如下：clear all format long x=[-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10]; y=[-1324 -994 -724 -508 -340 -214 -124 -64 -28 -10 -4 -4 -4 2 20 56 116 206 332 500 716]; =polyfit(x,y,3)运行后的结果为：p = 1.00000000000000 -3.00000000000000 1.99999999999999 -4.00000000000000 r = R: df: 17 normr: 3.184820221315369e-013故，拟合的三次函数为：y1=x.^3-3*x.^2+1.99999999999999*x-4我们再做出拟合后的函数图像与原来的散点图进行比较，看看拟合的效果；程序如下：clear all x=[-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10]; y1=x.^3-3*x.^2+1.99999999999999*x-4; y2=[-1324 -994 -724 -508 -340 -214 -124 -64 -28 -10 -4 -4 -4 2 20 56 116 206 332 500 716] plot(x,y1,x,y2,'r+')运行后得到的图像如下： 
 结果非常的理想。
[此贴子已经被作者于2008-2-11 13:09:11编辑过]

woshizhuimeng 发表于 2010-7-28 15:18

哇，太厉害了
顶一下
学到不少东西啊

xiaocongfei 发表于 2010-8-30 15:45

如果是更高次数的呢？如何观察它的图形？

Dustin_Keng 发表于 2012-9-7 21:20

就是，如果是毫无规律的呢？怎么办？

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[讨论]用matlab对一组数据拟合