No, I have no idea of what will be the degree of the number field in which
my spectral radius belongs to.
But if I could compute the characteristic polynomial of the matrix, I could
have the minimal polynomial of the spectral radius (and that's what I mean
by exact value).
Le jeudi 27 mars 2014
Do you have an idea of the expecting degree of the number field in
which your eigenvalue belongs to ? If yes you can use pari/GP
otherwise I do not see what you mean by exact value.
2014-03-27 11:17 UTC+01:00, Paul Mercat :
> OK, thank you, I see.
> It's an efficient method to compute a approximat
OK, thank you, I see.
It's an efficient method to compute a approximation of the spectral radius.
It's good but I still want to have the exact value. Maybe I can find the
exact value from the approximation ?
Le mercredi 26 mars 2014 23:56:49 UTC+1, vdelecroix a écrit :
>
> You compute powers but
You compute powers but *not* of the matrix itself ! You just compute
iteration of a single vector. Here is a rough implementation of what
you should do
sage: A = matrix([[1,2,3],[1,1,1],[1,0,1]])
sage: s = 0.
sage: v = random_vector(RDF,3)
sage: v /= v.norm()
sage: for i in xrange(100):
:
IIRC, the bottleneck to computing the spectra of large graphs is in
the construction of the adjacency matrix. I don't know why.
On Wed, Mar 26, 2014 at 3:28 PM, Paul Mercat wrote:
> Le mercredi 26 mars 2014 22:56:46 UTC+1, Dima Pasechnik a écrit :
>>
>> On 2014-03-26, Paul Mercat wrote:
>> >
>>
