Hi, I have developed a visual application to demonstrate the Runge phenomena and how to cure it (by Tchebychev approximation). It is inspired by the nice demonstration of the Taylor series you can find here: http://www.sagemath.org/tour-education.html
There is one part which computes the Newton interpolation:
def NewtonInterpolation(x,y,f):
poly=f[0]
q=1
s=f[0:len(f)]
stride=1
for k in range(len(f)-1,0,-1):
for i in range(k):
s[i]=(s[i+1]-s[i])/(y[i+stride]-y[i])
q*=(x-y[stride-1])
poly+=s[0]*q
stride+=1
return poly.factor()
and an other part, the interactive one, which starts by
@interact
The full code can be found here:
http://math.univ-lyon1.fr/~tdumont/sageproblems/
The result is very very slow... (about 10 seconds with 17 points -the
machine is slow -1ghz-).
I have tried different improvements:
-factorisation of the polynomial
-numerical computations (.n())
with very few results. It seems that the @interact part takes a lot of time.
Is there any possibility to improve it?
My other question:
If I look at what is running during the computation, I find that the
python interpreter is computing, but also the lisp (lisp.run). Why the
lisp ?
Yours, very sincerely.
--
Thierry Dumont. Institut Camille Jordan -- Mathematiques--
Univ. Lyon I,43 Bd du 11 Novembre 1918, 69622
- Villeurbanne Cedex - France.
[EMAIL PROTECTED] web: http://math.univ-lyon1.fr/~tdumont
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