Finding rank of large matrix, NOT sparse

[Jack P.]

I will need to find the rank of an integer matrix 208,012 x 208,012.
Is this feasible as is using linbox? This would be essentially a one-
time thing so as long as the runtime is something reasonable, I'm not
too concerned about efficiency here.
Thanks,
-Jack

[Jean-Guillaume Dumas]

Dear Jack I guess we would need more information:
is the matrix somewhat structured (so that e.g. storage and/or
matrix-vector product can be specialized, ...) ?
Otherwise for a generic dense no structure matrix of that size, the
number of coefficients to store is more that 43 bn,
the expected complexity 9 millions of billions operations and thus
already a computation modulo 2 would not be trivial.
Best,

--
Jean-Guillaume Dumas.
____________________________________________________
Jean-Guill...@imag.fr Tél.: +353 1 716 5318
Université Joseph Fourier Grenoble, France.
Claude Shannon Institute, University College Dublin,
CASL 1J, Belfield, Dublin 4, Ireland.
http://ljk.imag.fr/membres/Jean-Guillaume.Dumas
____________________________________________________

[David Saunders]

We are working (slowly) on a project to compute rank of a million by
million dense matrix, so this is a good stepping stone toward that
size.

Are the entries small? (eg. just 0s and 1s?). That can help.

Is the rank expected to be small (eg. less thank 30,000)? We have a
special technique for that.

Are the entries generated by formula? This can help with memory
management.

-dave

Jack P. wrote:
> I will need to find the rank of an integer matrix 208,012 x 208,012.
> Is this feasible as is using linbox? This would be essentially a one-
> time thing so as long as the runtime is something reasonable, I'm not
> too concerned about efficiency here.
> Thanks,
> -Jack
>
> >

On Nov 4, 12:17 pm, Jean-Guillaume Dumas <Jean-

Guillaume.Du...@imag.fr> wrote:
> Jack P. wrote:
> > I will need to find the rank of an integer matrix 208,012 x 208,012.
> > Is this feasible as is using linbox?  This would be essentially a one-
> > time thing so as long as the runtime is something reasonable, I'm not
> > too concerned about efficiency here.
> > Thanks,
> > -Jack
>
> Dear Jack I guess we would need more information:
> is the matrix somewhat structured (so that e.g. storage and/or
> matrix-vector product can be specialized, ...) ?
> Otherwise for a generic dense no structure matrix of that size, the
> number of coefficients to store is more that 43 bn,
> the expected complexity 9 millions of billions operations and thus
> already a computation modulo 2 would not be trivial.
> Best,
>
> --
>                                Jean-Guillaume Dumas.
> ____________________________________________________

> Jean-Guillaume.Du...@imag.fr   Tél.: +353 1 716 5318