Homework 13, Least Squares Fitting (16 points)

Now that you are comfortable with using SGEFA and SGESL to solve a set of linear equations, its time to do a real problem.

The file visc.tab contains viscosity data at selected temperatures. Each line contains first a temperature and second the corresponding viscosity. We've already dealt with this as an exercise in interpolation. This time I want you to generate a Least Squares approximation to the viscosity data. Modify the program cubefit.f to approximate the viscosity as a cubic polynomial (c0+c1*T+c2*T**2+ c3*T**3).

I want you to do three things to cubefit.f. First modify the subroutine "getdata" so that it asks the user for the name of the file containing data pairs. Second, add a subroutine named "cubicfit" to actually do the least squares fit. I recommend that you simply modify the subroutine quadfit. Finally, create a separte file named "linpack.f" containing all of the LINPACK subroutines that you obtained for Homework 13. Compile your program with the command "f77 cubefit.f linpack.f".

Leave the file cubefit.f in your homework directory.

Grading will be as follows:

I get the following answers when running my solution:

 Fit to 3rd order polynomial has a mean error of 2.50719E-05
 For the equation:
 y = coef(0) + coef(1)*x + coef(2)*x**2 + coef(3)*x**3
 coef(0) =   1.6147330E-02
 coef(1) =  -1.3551170E-04
 coef(2) =   3.8962528E-07
 coef(3) =  -3.7671630E-10

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