How to find the polynomial coefficients of two Array
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I have such data from a thesis as below:
x=[1/1800,1/60,1/3,1,2,4,8,24];
y1=[0.7291,3.1663,4.3217,6.5508,9.1189,16.2679,30.3524,44.7320];
y2=[0.4572,1.7790,5.2580,13.7910,30.1775,64.9784,109.7704,136.0388];
The author said he can get the chart as below after smooth processing the data.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/148163/image.gif)
Also,he can get the Polynomial coefficients:
r1 = 3. 550, 1. 788, 0. 6734, - 0. 09003, 0. 004448, 9. 396e-5, 6. 675e-7
r2= 1. 709, 8. 714, 4. 178, - 0. 8004, 0. 05731, - 0. 001856, 2. 277e- 5
I can figure out the chart by using
xi = 0:0.1:25;
yi1 = interp1(x,y1,xi,'pchip');
yi2 = interp1(x,y2,xi,'pchip');
plot(xi,yi1,'b:',xi,yi2,'r-');
This is the picture:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/148165/image.jpeg)
However, i get the Polynomial coefficients as below:
py1= polyfit(xi,yi1,6);
py2= polyfit(xi,yi2,6);
py1 =
0.0000 -0.0002 0.0056 -0.0851 0.4458 3.1673 1.4525
py2 =
0.0000 -0.0016 0.0498 -0.6844 3.3783 10.8772 0.1662
the Polynomial coefficients were quite different from the author's.
I don't konw if i missed any steps or which step is wrong.
I think maybe the error is happened when smooth processing the data.The author didn't tell which method he used to processing the data, while i just used the interp1 method.
I want to get the same coeffcients as the author.Any sugguestion about the processing method?
Any help would be kindly, many thanks!
1 Comment
Matt J
on 2 Jun 2013
I think maybe the error is happened when smooth processing the data.The author didn't tell which method he used to processing the data, while i just used the interp1 method.
Interpolation doesn't smooth the data in any way.
Accepted Answer
Matt J
on 2 Jun 2013
Edited: Matt J
on 2 Jun 2013
the Polynomial coefficients were quite different from the author's.
You're using a very small amount of data to perform the fit (only 1 more data point than the number of unknown coefficients).
In addition, it's a 6th-order polynomial. Fitting at an order that high is starting to get fairly ill-conditioned,
>> cond(vander(0:6))
ans =
1.5973e+06
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