[NumPy-Tickets] [NumPy] #2208: chebval: subtract half of first coefficient?

NumPy Trac numpy-tickets@scipy....
Sat Sep 1 11:47:17 CDT 2012


#2208: chebval: subtract half of first coefficient?
-------------------------------+--------------------------------------------
  Reporter:  smeared ink       |       Owner:  charris          
      Type:  defect            |      Status:  closed           
  Priority:  normal            |   Milestone:  1.8.0            
 Component:  numpy.polynomial  |     Version:  devel            
Resolution:  invalid           |    Keywords:  chebyshev chebval
-------------------------------+--------------------------------------------
Changes (by charris):

  * status:  new => closed
  * resolution:  => invalid


Comment:

 No. The reference you give determines the Chebyshev coefficients for
 fitting a function using the Chebyshev points of the first kind over which
 the Chebyshev polynomials are orthogonal, but not normalized. The factor
 of N/2 shown at the link accounts for the lack of normalization except for
 the T_0 term, which needs an extra factor of .5. Because the chebval
 function evaluates  series, you need to correct the c_0 coefficient
 determined the NR way before calling chebval. Alternatively, you can fix
 the normalization factor for the T_0 term up front if you are using a
 matrix multiply to fit a large number of functions.

 Perhaps I should add a function approximation method to the classes.
 Hmm...

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Ticket URL: <http://projects.scipy.org/numpy/ticket/2208#comment:1>
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