Polyfit with scaling

[Ben Abbott]

On Feb 3, 2008, at 7:50 PM, Dmitri A. Sergatskov wrote:

> On Feb 3, 2008 6:20 PM, Ben Abbott <bpabbott at mac.com> wrote:
>
>> Give these results and the need to remain compatible with past  
>> expectations,
>> and with Matlab, I'm inclined to make both QR and normalization  
>> optional.
>>
>
> In that case can we just leave things as they are and perhaps just  
> add some
> words to help file? (May be also pointing to the wpolyfit file).
> I am curious to see how well Matlab handles your benchmark.


Regarding leaving things as they are, the normalization is not  
something I'd expect most users to desire to handle for themselves.

However we might either provide for optional normalization, or provide  
the routines to do so.

Regarding how Matlab handles this benchmark here are the results.

                        Matlab
  N   M     norm(y-yfit)        norm(p-fit)
  1   2    2.542114973e-13    2.955859084e-12
  1   3    3.410605132e-13    1.693934712e-11
  2   3    1.028152284e-09    1.323761177e-06
  2   4    4.440674381e-10    3.319473118e-06
  2   5    4.939083810e-10    4.947078972e-06
  3   4    2.189135306e-06    5.694889319e+00
  3   5    1.099055345e-06    2.955133100e+00
  3   6    7.348554138e-07    3.296905699e+00
  3   7    1.217871795e-06    5.411753547e+00
  4   5    1.196039913e-03    2.780029492e+06
  4   6    2.441406250e-03    9.003165440e+05
  4   7    3.895778546e-03    4.993247502e+06
  4   8    3.054689407e-03    5.591453444e+05
  4   9    1.708984375e-03    3.790911374e+05

Matlab's results appear consistent with QR without normalization.

Ben

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