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Why is the polyval command giving two different answers?

4 vues (au cours des 30 derniers jours)
Baldemy
Baldemy le 22 Sep 2014
Commenté : Matt J le 23 Sep 2014
Why does the polyval operator not work as expected. Is the ans variable not stored as a column vector? Why aren't the second, fifth, and sixth results equal?
>> roots([1,-8,17,2,-24])
ans =
4.0000
3.0000
2.0000
-1.0000
>> polyval([1.-8,17,2,-24],ans)
ans =
-192.0000
-54.0000
-8.0000
-2.0000
>> roots([1,-8,17,2,-24])
ans =
4.0000
3.0000
2.0000
-1.0000
>> x=ans
x =
4.0000
3.0000
2.0000
-1.0000
>> polyval([1,-8,17,2,-24],x)
ans =
1.0e-13 *
0.8882
0.3197
0.0355
0.1421
>> polyval([1,-8,17,2,-24],[2.0000;3.0000;-1.0000;3])
ans =
0
0
0
0

Réponse acceptée

Alberto
Alberto le 22 Sep 2014
Instruction roots uses an iterative numeric method to approximate the solution in float arithmetic. What you get is an excellent approximation.
If you need the exact solution you should try a symbolic method:
g = x^4-8*x^3 + 17*x^2 +2*x -24
g =
x^4 - 8*x^3 + 17*x^2 + 2*x - 24
>> sol=solve(g==0)
sol =
2
3
4
-1
  1 commentaire
Matt J
Matt J le 23 Sep 2014
You also may need a symbolic version of polyval, even when you have the exact roots:
>> polyval([1,-8,17,2,-24]/3,[4 3 2 -1])
ans =
1.0e-14 *
0.8882 0.1776 0.1776 0.1776

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Plus de réponses (1)

Matt J
Matt J le 22 Sep 2014
Modifié(e) : Matt J le 22 Sep 2014
Because you have a typo in your call to polyval: a period appears where a comma should be.
  2 commentaires
Baldemy
Baldemy le 22 Sep 2014
Modifié(e) : Matt J le 22 Sep 2014
ok then this happens instead
>> roots([1,-8,17,2,-24])
ans =
4.000000000000009
2.999999999999992
2.000000000000001
-1.000000000000000
>> polyval([1,-8,17,2,-24],ans)
ans =
1.0e-13 *
0.888178419700125
0.319744231092045
0.035527136788005
0.142108547152020
Matt J
Matt J le 22 Sep 2014
Modifié(e) : Matt J le 22 Sep 2014
And what don't you like about it? The result is quite close to zero, as one would expect.

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