[Numpy-tickets] [NumPy] #664: more accurate representation of polynomials
NumPy
numpy-tickets@scipy....
Fri Feb 22 15:08:04 CST 2008
#664: more accurate representation of polynomials
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Reporter: pv | Owner: somebody
Type: enhancement | Status: new
Priority: normal | Milestone: 1.1
Component: numpy.lib | Version: none
Severity: normal | Resolution:
Keywords: |
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Comment (by charris):
Polynomials represented as power series are inherently ill conditioned. If
you want accuracy for high degree polynomials use Chebyshev polynomial
expansions. Don't convert the Chebyshev representation to a polynomial,
you will lose all the numerical advantages if you do so, instead evaluate
the expansion using backward recursion. Backward recursion, of which
Horner's method is a special case, is useful for evaluting polynomial
series whose terms are defined recursively.
What you need is a complete Chebyshev package. I posted my own Chebyshev
package on the Numpy developer's list sometime back. If you search the
list you may find it. There were actually two postings, you will want the
last one. Perhaps that package could be adapted to use parts of the SciPy
Chebyshev package, at the moment it is written in pure Python/Numpy. In
any case, such a package shouldn't be part of Numpy. Polynomials really
don't belong in Numpy either.
--
Ticket URL: <http://scipy.org/scipy/numpy/ticket/664#comment:1>
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