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Not clear result of approximation
http://forum.alglib.net/viewtopic.php?f=2&t=321		 Page 1 of 1
Author:  aym53 [ Tue Mar 15, 2011 10:25 am ]
Post subject:  Not clear result of approximation
Hi all. There is a problem.
I have tried to approximate a polynom of the third order
y:=-39.692 - 1.7902e-3*x + 1.8854e-7*x^2-8.4099e-12*x^3 by means of
a polynom of the third order. Used function LSFitLinear.
The result of approximation is resulted in drawing.
Attachment:
m1.JPG
m1.JPG [ 29.31 KiB | Viewed 5445 times ]

Blue color - initial function. Lilac - result of approximation.
The example of approximation of a tangent resulted on a site works normally.
I use ALGLIB with Delphi 7.
In what the reason of such result?
Author:  Sergey.Bochkanov [ Tue Mar 15, 2011 7:24 pm ]
Post subject:  Re: Not clear result of approximation
I think that it is ill-conditioning issue. Maybe it is better to use Chebyshev polynomials as basis functions - at least for intermediate calculations.

What is the value of TaskRCond field of solver report?
Author:  aym53 [ Wed Mar 16, 2011 5:30 am ]
Post subject:  Re: Not clear result of approximation
The value of TaskRCond=5.92e-10.
I did such experiment: such values of function to set in points 0,1,2. 18.
Approximation was magnificent. Possibly reason in great values of argument. Whether there is a way to solve a problem within the limits of application Lsfitlinear?
Author:  Sergey.Bochkanov [ Wed Mar 16, 2011 5:38 am ]
Post subject:  Re: Not clear result of approximation
TaskRCond=5.92e-10 means that your problem is very badly conditioned. You have two ways to solve this issue:
* quick and dirty way - linearly map your points to [-1,+1], calculate approximation, then transform polynomial back to [0,12000]
* more efficient, but complex solution - linearly map your points to [-1,+1], calculate approximation using Chebyshev basis, then transform polynomial back to power basis and scale X to be in [0,12000].
Author:  aym53 [ Wed Mar 16, 2011 6:26 am ]
Post subject:  Re: Not clear result of approximation
All has understood. Thanks.
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