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
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
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 co
On Mon, 06 Jul 2009 16:53:42 +0200
Fabrice Silva 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 Hermitean
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 w
On Mon, Jul 6, 2009 at 8:16 AM, Charles R Harris
wrote:
>
>
> On Mon, Jul 6, 2009 at 3:44 AM, Fabrice Silva 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
On Mon, Jul 6, 2009 at 3:44 AM, Fabrice Silva 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 values becomes s
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 2009-07-03, Charles R Harris 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 machine
precision, anothe
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
On Fri, Jul 3, 2009 at 3:48 AM, Fabrice Silva 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
> than 20, and then h
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 -2.44499178e+
On Fri, 03 Jul 2009 14:26:39 +0200
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, s
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
On Fri, 03 Jul 2009 11:48:45 +0200
Fabrice Silva 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
> than 20,
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 so
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