Re: fixed points piecewise-linear fitting

[c.]

On 18 Mar 2012, at 00:42, Juan Pablo Carbajal wrote:

> If you accept the min square idea (which makes a lot of sense). You
> are solving what any FEM in 1D would solve when using linear elements
> center in your Yf. You are projection your (X,Y) function into the
> tent space. I will search my teaching code. I have a function to do it
> somewhere there. In the meanwhile somebody could update us about FEM
> 1D in Octave?
> Maybe Carlo knows about this.

bim does do piecewise-linear finite elements but it uses only trapezoidal rule
for computing integrals (in order to obtain mass-lumping) so using it for L2 
projection
would be essentially equivalent to sampling data at the grid nodes.

geopdes [1] might be better at this and produce a smoother interpolating 
function. 
I never used it for 1d problems but it should work with at most a very few 
tweaks.

Ben's solution should also be OK if you just care about the result and not 
about the algorithm. 
HTH,
Carlo

[1] http://sourceforge.net/projects/geopdes/