Re: [Bug-gsl] Re: infinite loop in gsl_eigen_symm

[Andries E. Brouwer]

On Thu, Aug 30, 2007 at 02:59:41PM +0100, Brian Gough wrote:

> Thanks for the suggestion, I will add a short discussion of this to
> the manual.  The algorithm is symmetric bidiagonalization followed by
> QR reduction (see Golub & Van Loan, "Matrix Computations" (3rd ed),
> Section 8.3 for details).  The eigenvalues are accurate to an absolute
> error of eps*||A||_2, where eps = double precision accuracy.

Thanks!

> > (It is easy to compute the exact eigenvalues in the example I gave.
> > They are 0 with multiplicity 21, +-3sqrt{3}, +-(1+-sqrt{13})/2.)
> 
> For the matrix you sent, I get a different characteristic polynomial
> (via pari/gp's matdet function)  p(u)=u^21 (u^6 -25*u^4 + 134*u^2 - 159) 

Ah, yes, I see - sorry about that.

Andries