Le lundi 06 juillet 2009 à 17:57 +0200, Fabrice Silva a écrit :
Le lundi 06 juillet 2009 à 17:13 +0200, Nils Wagner a écrit :
IIRC, the coefficients of your polynomial are complex.
So, you cannot guarantee that the roots are complex
conjugate pairs.
Correct! If the construction is done
Le vendredi 03 juillet 2009 à 10:00 -0600, Charles R Harris a écrit :
What do you mean by erratic? Are the computed roots different from
known roots? The connection between polynomial coefficients and
polynomial values becomes somewhat vague when the polynomial degree
becomes large, it is
On Mon, Jul 6, 2009 at 3:44 AM, Fabrice Silva si...@lma.cnrs-mrs.fr wrote:
Le vendredi 03 juillet 2009 à 10:00 -0600, Charles R Harris a écrit :
What do you mean by erratic? Are the computed roots different from
known roots? The connection between polynomial coefficients and
polynomial
On Mon, Jul 6, 2009 at 8:16 AM, Charles R Harris
charlesr.har...@gmail.comwrote:
On Mon, Jul 6, 2009 at 3:44 AM, Fabrice Silva si...@lma.cnrs-mrs.frwrote:
Le vendredi 03 juillet 2009 à 10:00 -0600, Charles R Harris a écrit :
What do you mean by erratic? Are the computed roots different
Le lundi 06 juillet 2009 à 08:16 -0600, Charles R Harris a écrit :
Double precision breaks down at about degree 25 if things are well
scaled, so that is suspicious in itself. Also, the companion matrix
isn't Hermitean so that property of the roots isn't preserved by the
algorithm. If it were
On Mon, 06 Jul 2009 16:53:42 +0200
Fabrice Silva si...@lma.cnrs-mrs.fr wrote:
Le lundi 06 juillet 2009 à 08:16 -0600, Charles R Harris
a écrit :
Double precision breaks down at about degree 25 if
things are well
scaled, so that is suspicious in itself. Also, the
companion matrix
isn't
Le lundi 06 juillet 2009 à 17:13 +0200, Nils Wagner a écrit :
IIRC, the coefficients of your polynomial are complex.
So, you cannot guarantee that the roots are complex
conjugate pairs.
Correct! If the construction is done with X1 and X1* treated separately,
the coefficients appear to be
Le lundi 06 juillet 2009 à 17:57 +0200, Fabrice Silva a écrit :
Le lundi 06 juillet 2009 à 17:13 +0200, Nils Wagner a écrit :
IIRC, the coefficients of your polynomial are complex.
So, you cannot guarantee that the roots are complex
conjugate pairs.
Correct! If the construction is done
Hello
Has anyone looked at the behaviour of the (polynomial) roots function
for high-order polynomials ? I have an application which internally
searches for the roots of a polynomial. It works nicely for order less
than 20, and then has an erratic behaviour for upper values...
I looked into the
On Fri, 03 Jul 2009 11:48:45 +0200
Fabrice Silva si...@lma.cnrs-mrs.fr wrote:
Hello
Has anyone looked at the behaviour of the (polynomial)
roots function
for high-order polynomials ? I have an application which
internally
searches for the roots of a polynomial. It works nicely
for order
Le vendredi 03 juillet 2009 à 11:52 +0200, Nils Wagner a écrit :
You will need multiprecision arithmetic in that case.
It's an ill-conditioned problem.
I may have said that the solution are of the same order of magnitude, so
that the ratio between the lowest and the highest absolute values of
Le vendredi 03 juillet 2009 à 14:43 +0200, Nils Wagner a écrit :
Just curious - Can you provide us with the coefficients of
your polynomial ?
Working case :
Polynomial.c =
[ -1.34100085e+57 +0.e+00j -2.28806781e+55 +0.e+00j
-4.34808480e+54 -3.27208577e+36j
On Fri, Jul 3, 2009 at 3:48 AM, Fabrice Silva si...@lma.cnrs-mrs.fr wrote:
Hello
Has anyone looked at the behaviour of the (polynomial) roots function
for high-order polynomials ? I have an application which internally
searches for the roots of a polynomial. It works nicely for order less
Fabrice Silva wrote:
Le vendredi 03 juillet 2009 à 11:52 +0200, Nils Wagner a écrit :
You will need multiprecision arithmetic in that case.
It's an ill-conditioned problem.
I may have said that the solution are of the same order of magnitude, so
that the ratio between the lowest and the
On 2009-07-03, Charles R Harris charlesr.har...@gmail.com wrote:
roots? The connection between polynomial coefficients and polynomial values
becomes somewhat vague when the polynomial degree becomes large, it is
numerically ill conditioned.
In addition to switching to higher precision than
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