- Fitting a cubic to the data by using MATLAB. For the given data points;
- Evaluate the cubic on the data and plot
- Fitting a non-linear curve to the data with least-square method.
- Use the data in the previous item.
- We will fit
.
- Repeat each of the steps given in the following solution by hand.
Solution:
- First, we should compute a new table with
Then our new data points;
- Construct the normal equations (with and )
- Dividing each of these equations by and expanding the summation, we get the so-called normal equations
- Solve these normal equations to find and
- So; we obtained and , we should convert back to the original variables. Convert back to the original variables
we have
- Plot vs and vs then compare them. For plotting (see Fig. 1);
Figure 1:
plot(x,Y,'o',x,y,'-').
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- Compare this least-square polynomial results with the built-in MATLAB functions results in the previous item (item 1), see Fig.2.
Figure 2:
plot(x,Y,'o',x,f,'-',x,y,'+').
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Cem Ozdogan
2010-12-13