Overshoot

I would like some advice on this

N=10 1 2 3 4 5 6 7 8 9 10 0 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 1:10

Odd numbers perhaps, but it illustrates an overshoot after the first 8.75.

With the number you have given then any interpolation scheme will do the same, these systems don't like sharp corners. Even a very higher order polynomial, or Fourier approach (I've yet to write these but will), will have local overshot.

Therefore what you have to do is locally force conformity, it'll require a little bit of experimentation, but try this:

N=12 1 2 2.1 2.2 3 4 5 6 7 8 9 10 0 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 1:10

I've bolded the two extra terms (I hope you see these at 2.1 and 2.2).

Does anyone know of any algorithm that will evaluate a "closeness of fit"?

For example, I have two stored cubic splines that I want to compare to a new spline and pick the one that is closer.

Any thoughts?

Typical approach is to look at the Root Mean Squares (RMS), something like: where

• f(x) is say your fitted function
• g(x) are your original points

Obviously you select values of x that are at know points in g(x) and apply to f(x).

Consider this example

double f[4]={1,2,3,4};      // approx values (say)
  double g[4]={1.1,2,2.9,4};  // real values
 
  double RMS=0;
  for(int i=0;i<4;i++) RMS+=pow(f[i]-g[i],2);
  RMS=sqrt(RMS/4.0);