RE: One question to everybody

[Tuan Pham <tuan.pham@unsw.edu.au>]

Hi

In answer to question 2:

With 1 point you can fit a 0-th order polynomial (constant),
with 3 points a 1st order p. (plane)
with 6 points a 2nd order p., etc.
It's easy to solve for the coefficients by matrix inversion.
For intermediate number of points the problem is underdefined
e.g. through 2 points you can fit an infinite number of planes.

Cheers
Tuan Pham


>I have a good friend who is socjologist and he has one question to you: 
>Consider the following elementary problem (interpolation's problem):
>Given n points in the Euclides space R^{3}. Find a smooth (minimal) 
>
>Questions: 1) Is there a grafical program which can do that? (mathematica,
>              plot, ...)
>           2) If we want to find a polynomial of 2 variables
>              which has a graph containing n points, then are
>              expressions of polynomial's coefficients known?   
>
>Please a quick answear.
>SN
>
>BTW. The similar 2-dimensional problems are Newtonian and
>     Lagrangian. 
>