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¶å¾å½¢ä¸ºä¸æ²çº¿ï¼ä½¿å¨å离æ£ç¹ä¸å°½å¯è½æ¥è¿ç»å®çå¼ï¼è¿ä¸è¿ç¨ç§°ä¸ºæ²çº¿æåãæ常ç¨çæ²çº¿æåæ¹æ³æ¯æå°äºä¹æ³ï¼è¯¥æ¹æ³æ¯å¯»æ¾å½æ°ä½¿å¾æå°ã
MATLABå½æ°ï¼p=polyfit(x,y,n)
[p,s]= polyfit(x,y,n)
说æï¼x,y为æ°æ®ç¹ï¼n为å¤é¡¹å¼é¶æ°ï¼è¿åp为å¹æ¬¡ä»é«å°ä½çå¤é¡¹å¼ç³»æ°åépãxå¿
é¡»æ¯åè°çãç©éµsç¨äºçæé¢æµå¼ç误差估计ã(è§ä¸ä¸å½æ°polyval)
å¤é¡¹å¼æ²çº¿æ±å¼å½æ°ï¼polyval()
è°ç¨æ ¼å¼ï¼ y=polyval(p,x)
[y,DELTA]=polyval(p,x,s)
说æï¼y=polyval(p,x)为è¿å对åºèªåéxå¨ç»å®ç³»æ°Pçå¤é¡¹å¼çå¼ã
[y,DELTA]=polyval(p,x,s) 使ç¨polyfitå½æ°çé项è¾åºså¾åºè¯¯å·®ä¼°è®¡YDELTAãå®å设polyfitå½æ°æ°æ®è¾å
¥ç误差æ¯ç¬ç«æ£æçï¼å¹¶ä¸æ¹å·®ä¸ºå¸¸æ°ãåYDELTAå°è³å°å
å«50%çé¢æµå¼ã
ç»ä¹ :å¦ä¸ç»å®æ°æ®çæåæ²çº¿ï¼x=[0.5,1.0,1.5,2.0,2.5,3.0]ï¼
y=[1.75,2.45,3.81,4.80,7.00,8.60]ã
解ï¼MATLABç¨åºå¦ä¸ï¼
x=[0.5,1.0,1.5,2.0,2.5,3.0];
y=[1.75,2.45,3.81,4.80,7.00,8.60];
p=polyfit(x,y,2)
x1=0.5:0.05:3.0;
y1=polyval(p,x1);
plot(x,y,'*r',x1,y1,'-b')
计ç®ç»æ为ï¼
p =0.5614 0.82871.1560
å³æå¾å¤é¡¹å¼ä¸ºy=0.5614x^2+0.08287x+1.15560
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åµããmatlab polyfit ååºæ¥çå¼ä»å·¦å°å³è¡¨ç¤ºä»é«æ¬¡å°ä½æ¬¡çå¤é¡¹å¼ç³»æ°ããç»ä¸ªä¾åä¸çå°±ç¥éäºããx = (0: 0.1: 2.5)';ããy = erf(x);ããp = polyfit(x,y,6)ããp =ãã0.0084 -0.0983 0.4217 -0.7435 0.1471 1.1064 0.0004ããåy=0.0084x^6-0.0983x^5+0.4217x^4-0.7435x^3+0.1471x^2+1.1064x+0.0004ãã解é2ï¼ããMATLAB软件æä¾äºåºæ¬çæ²çº¿æåå½æ°çå½ä»¤ï¼ããå¤é¡¹å¼å½æ°æåï¼a=polyfit(xdata,ydata,n)ããå
¶ä¸n表示å¤é¡¹å¼çæé«é¶æ°ï¼xdataï¼ydata为å°è¦æåçæ°æ®ï¼å®æ¯ç¨æ°ç»çæ¹å¼è¾å
¥ï¼è¾åºåæ°a为æåå¤é¡¹å¼y=a1xn+...+anx+a n+1çç³»æ°ããå¤é¡¹å¼å¨xå¤çå¼yå¯ç¨ä¸é¢ç¨åºè®¡ç®ï¼ããy=polyval(a,x,m)ãã线æ§ï¼m=1, äºæ¬¡ï¼m=2, â¦ããpolyfitçè¾åºæ¯ä¸ä¸ªå¤é¡¹å¼ç³»æ°çè¡åéã为äºè®¡ç®å¨xiæ°æ®ç¹çå¤é¡¹å¼å¼ï¼è°ç¨MATLABçå½æ°polyvalãããä¾ï¼ããx=0:0.1:1; y=[-0.447 1.978 3.28 6.16 7.08 7.34 7.66 9.56 9.489.30 11.2];
polyfitç¨æ³ç¤ºä¾ç»æ
A=polyfit(x,y,2)ããz=polyval(A,x);ããplot(x,y,'r*',x,z,'b')ããéçï¼ããå¨ä¸å°ä¹¦ä¸å论åä¸ï¼polyfit被误åä½âployfitâï¼ä½¿å¾å¾å¤åå¦è
误解ï¼è®¤ä¸ºèªå·±å®è£
çMATLAB软件åºéï¼æ æ³æ¾å°è¿æ ·çå½æ°ãåªè¦æ³¨ææ¼åæ£ç¡®å³å¯ãåæ ·å°ï¼polyvalå½æ°ä¹æ被误å为âployvalâã
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