Re: [Mplapack-devel] Can I compute eigenvalues of ill-conditioned matrix less than 10^-156 ?
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From: Gang Y. <ee...@gm...> - 2011-09-13 03:40:12
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Hi, Tomonori, Thank you very much. Yes, for very ill-conditioned matrices, eigenvalues are very sensitive to round-off errors when computing with float-point. I think I can obtain the smallest eigenvalues if using higher precision arithmetic. best, gang On Mon, Sep 12, 2011 at 11:01 PM, Tomonori Kouya <ju...@qu...>wrote: > Hi, Gang. I have tried to solve some eigenvalue problems using MPFR/GMP. > > Very ill-conditionded matrices such as Hilbert or Lotkin matrices, are > too sensitive to keep their theoretical properties due to initial error > or round-off error in computing process. In case of Hilbert matrix, it > is theoretically positive definite but some of smallest eigenvalues can > be minus due to initial error in approximated elements of Hilbert matrix. > > I recommend to know how sensitive your matrix is for such error by using > variable precision of MPFR/GMP in order to solve your troubles. > > (2011/09/12 23:35), Gang Yan wrote: > > Now I have a problem when I calculate the eigenvalues of an extremely > > ill-conditioned matrix, in a problem of control system research. The > matrix > > is not very large, e.g., 30X30, but extremely ill-conditioned, i.e., > having > > the largest eigenvalue ~10^-2 and the smallest eigenvalue> 10^-156. I > found > > that the eigenvalue programme using GMP or MPFR can only compute > eigenvalues > > <10^-156, or I will get some minus eigenvalues which is not wrong because > > the matrix is positive-definition. I use a 64-bit notebook. > > > ------------------------------------------------------------------------------ > Doing More with Less: The Next Generation Virtual Desktop > What are the key obstacles that have prevented many mid-market businesses > from deploying virtual desktops? How do next-generation virtual desktops > provide companies an easier-to-deploy, easier-to-manage and more affordable > virtual desktop model.http://www.accelacomm.com/jaw/sfnl/114/51426474/ > _______________________________________________ > Mplapack-devel mailing list > Mpl...@li... > https://lists.sourceforge.net/lists/listinfo/mplapack-devel > |