Re: [Mplapack-devel] Can I compute eigenvalues of ill-conditioned matrix less than 10^-156 ?

[Gang Y. <ee...@gm...>]

Many thanks, Maho. Attached please find the source code.

A20.dat is the input matrix, eigenvalue_mpfr.cpp is the source code modified
from your example code.

Place the two files into the folder mpack-0.6.7/examples/mlapack/ and use
commands "make" and  "./eigenvalue_mpfr",  it will show the results of the
largest and smallest eigenvalues.
It is shown that when the variable tt (a time variable in my program) is
very small, the matrix will become extremely ill-conditioned, and the
smallest eigenvalue will be less than 1e-156 and thus become negative.

thanks,
gang

On Mon, Sep 12, 2011 at 11:53 PM, Maho NAKATA <ch...@ma...> wrote:

> From: Gang Yan <ee...@gm...>
> Subject: Re: [Mplapack-devel] Can I compute eigenvalues of ill-conditioned
> matrix less than 10^-156 ?
> Date: Tue, 13 Sep 2011 11:45:47 +0800
>
> > Hi, Maho,
> >
> >
> > Gang, if you want to use MPACK, as Kouya-sensei wrote, please use
> >> GMP or MPFR version (to enlarge your precision).
> >>
> > I published a tutorial in Japanese (sorry), and
> >> I'll upload to the web page when I can publish my original one at the
> web.
> >
> >
> >> In the mean time, if you can use GMP version and setting
> >> MPACK_GMP_PRECISION environment variable to change pricision
> dynamically.
> >>
> >
> >
> > Yes, I used the GMP and MPFR version and tuned the precision variable
> from
> > 256 to 2048, but the results are truncated at ~10^-156. When the
> eigenvalues
> > are smaller than ~10^-156, they will become negative. How can I improve
> the
> > precision beyond 10^-156? Thanks.
>
> Hm, could you please check your inputs, so that not to include trancated
> values.
> or could you please send me your source codes.
>
> thanks
>  Nakata Maho
>