[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
 Reporter:  pv           |        Owner:  somebody
     Type:  enhancement  |       Status:  new     
 Priority:  normal       |    Milestone:  1.1     
Component:  numpy.lib    |      Version:  none    
 Severity:  normal       |   Resolution:          
 Keywords:               |  
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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