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please help solve generalized eigen problems

PostPosted: Thu Nov 17, 2005 4:23 am
by phygjd
I am going to solve
where A and B are both tridiagonal matrixs, X is a vector, E the eigenvalue. According to my problem, one eigenvalue is zero and other eigenvalues must be positive. However, NOT all the numerical eigenvalues are positive!

In my project, B is positve definite, while A is not positive definite. The diagonal elements of A and B are not quite small, while subdiagonal and superdiagonal elments are quite samll (~10^-5). I first factorize B using DPOTRF, second reduce the problem to a standard problem using DSYGST, then I use DSYTRD, finally I use DSTEBZ to get all the eigenvalues. I have tested my subroutine of solving generalized eigen problems using some other A and B, and found the the subroutine is correct. However, when I used the form of A and B in my problem, I cannot get the correct answer. Is it due to the fact that the sub- and super- diagonal elements in my problem is small so that numerical error is quite large in the calculation.

Re: please help solve generalized eigen problems

PostPosted: Fri Nov 18, 2005 6:39 am
by sven
In general small eigenvalues may be poorly determined and, in particular, a zero eigenvalue is unlikely to be computed as zero. It is better to remove zero eigenvalues at the modelling stage, if that is possible.

Section 4.10 of the LAPACK Users' Guide gives information on error bounds for the generalized symmetric definite eigenproblem, and gives a code fragment illustrating how to compute the error bounds. By the way, you can use DSYGV to solve your problem, rather than putting all the computational parts together yourself.