Re: [Mplapack-devel] Can I compute eigenvalues of ill-conditioned matrix less than 10^-156 ?
Status: Pre-Alpha
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nakatamaho
From: Gang Y. <ee...@gm...> - 2011-09-22 21:10:05
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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 |