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

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

Hi Maho,

On Fri, Sep 23, 2011 at 4:59 AM, Maho NAKATA <ch...@ma...> wrote:

> Hi Gang,
>
> From: Gang Yan <ee...@gm...>
> Subject: Re: [Mplapack-devel] Can I compute eigenvalues of ill-conditioned
> matrix less than 10^-156 ?
> Date: Fri, 23 Sep 2011 00:55:35 +0800
>
> >   but the smallest eigenvalues as pointed out ~~~~~~~~~ are negative. So
> it
> > is wrong. I think the program can only compute the eigenvalues which are
> > larger than 1e-156 accurately. Do you think so? Or I am wrong for some
> > reasons? Thanks.
>
> in your case, you use
>
> > //initialization of MPFR
> >    int default_prec = 4096;
> >    mpfr_set_default_prec(default_prec);
>
>
 Yes.


> then, machine epsilon is approximately 7.458340731e-155 (*).
> In this case, relative errors of
> eigenvalues can be less accurate than 7.458340731e-155.
> you are doing something complicated in your program and
> I guess some rouding errors included. In my opinion,
> therefore, you found some small negative eigenvalues.
>
> (*) you can check this by inserting following code and rerun your
> program.
>    mpreal a = Rlamch_mpfr("E");
>    mpfr_out_str(stdout, 10, 10, a, MPFR_RNDN);
>    printf("\n");
> Thanks,
>

 I will check it. Many thanks.


> -- Nakata Maho http://accc.riken.jp/maho/ , JA OOO
> http://ja.openoffice.org/
> http://blog.goo.ne.jp/nakatamaho/ ,GPG:
> http://accc.riken.jp/maho/maho.pgp.txt
>

best,
gang