Polynomial approximation of a function

[Nathann Cohen]

Hello !!!

I remember there is an easy way ( through matrices ) to get the "best" approximation of a function by a polynomial of bounded degree ( and not only the usual approximation by a line ).... I looked for such functions in Sage, but found none... Does it mean there is not already in Sage some function to compute it ( it would be a shame !!! ), or just that I once more failed to look for a functio properly ( and that would be a shame, too.... )     :-)

Thank you for your help !!!

Nathann

[Laurent]

Nathalie Cohen ha scritto:

> Hello !!!
>
> I remember there is an easy way ( through matrices ) to get the "best"
> approximation of a function by a polynomial of bounded degree ( and not only
> the usual approximation by a line )....

Are you speaking about the Taylor expansion ?
If so, it is implemented in Sage, but I don't remember the exact names.
(searching for "Taylor" in the documentation)

have a good afternoon
Laurent

[Robert Bradshaw]

Are you thinking of Chebyshev polynomials? I don't think there is, but
there might be as part of scipy. I've got (two) implementations of
them that I haven't had time to put into Sage proper, but they're
pretty straightforward to implement.

- Robert

[Jason Grout]

Sage also includes mpmath, which appears to have appropriate functions:

http://mpmath.googlecode.com/svn/trunk/doc/build/calculus/approximation.html

Jason

[Nathann Cohen]

Thank you for your answers !!

I was thinking about some multidimensional linear approximation, where
the basis you use is ( for points of coordinates (x_i, y_i ) ) the
vectors
The family of x_i, x_i
The family of x_i, x_i^2
The family of x_i, x_i^3
The family of x_i, x_i^4
...

But it turns out Scipy was the asnwer.... Thank you very much :-)

Nathann

> http://mpmath.googlecode.com/svn/trunk/doc/build/calculus/approximati...
>
> Jason