Example 6.  Find the "least squares parabola" that for the four data points  .  

Solution 6.

(a). Write down the linear system AC = B to be solved.

(b). Solve the linear system for the coefficients using our  LUfactor[n]  and  SolveLU[n]  subroutines.

(c). Construct the polynomial  p[x].  The coefficients are stored in the array  c  and the elements are .

Of course we could do all this work in two lines by using Mathematica's built in    procedure.

We are done.

We can graph the polynomial, this is just for fun !

(c) John H. Mathews 2004