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<font face="Courier New">Stéphane, </font><br>
<br>
<blockquote type="cite"
cite="mid:0533e578-1226-e6df-a52b-ba6aa5a92bc4@utc.fr"><font
face="Courier New">Yeah, but really badly conditionned compared
to the above method which is based on orthogonal tranformations
(X=Q*R factorization). With your below method you solve a linear
system with X'*X matrix which has a condition number which is
the square of the condition number of the R matrix issued from
the Q*R factorization of X.</font></blockquote>
<br>
Thanks for the clarification!<br>
<br>
Is it posible to predict in what kind of cases will the bad
conditioning impact on the result? I've compared the results for
several cases and they are exactly the same. <br>
<br>
However, I've noticed that when taking the inverse of a matrix whose
components span several orders of magnitude there are important
errors, but if I manage to normalize the poblem the errors are
substantially reduced<br>
<br>
Regards,<br>
<br>
Federico<br>
<br>
<br>
<blockquote type="cite"
cite="mid:0533e578-1226-e6df-a52b-ba6aa5a92bc4@utc.fr">
<p><font face="Courier New">S.<br>
</font></p>
<blockquote type="cite"
cite="mid:208747ef-5ed7-4d7f-3883-391c60c2a804@fceia.unr.edu.ar"><font
face="Courier New"> <br>
The basic algorithm I use is (n = desired degree):<br>
<br>
// Initialize matrix X<br>
X = ones(length(x), n+1);<br>
// Compute Vandermonde's matrix<br>
for k =2:n+1<br>
X(:,k) = X(:,k-1).*x;<br>
end<br>
// Apply the Moore-Penrose pseudoinverse matrix and<br>
// multiply by the dependent data vector to get the<br>
// least squares approximation of the polynomial<br>
// coefficients<br>
A = inv(X'*X)*X'*y;<br>
<br>
I've seen some discussion regarding the need for a polyfit
function in Scilab. The main argument against such a function
is that it is unnecessary since it is a particular case of the
backslash division. This is true, but the above example shows
that users' implementations are not always optimized, and as
it is such a frequent problem, it would be nice to have a
native polyfit (or whatever it may be called) function. <br>
<br>
Regards,<br>
<br>
Federico Miyara<br>
</font> <br>
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<pre class="moz-signature" cols="72">--
Stéphane Mottelet
Ingénieur de recherche
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
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