🚀 go-pugleaf

In article <1993Jan22.090701.11440@vax.oxford.ac.uk> nagrwb@vax.oxford.ac.uk writes:
>In article <20JAN199313260117@envmsa.eas.asu.edu>, sychen@envmsa.eas.asu.edu (Chen, Shen Yeh) writes:
>> 
>>    I need to solve a linear system equation. In fact, that's the stiffness
>>  matrix [K] from finite element method. The system is like :
>>  [K]*{U}={P}.  where [K](nxn)
>> 
>>    [K] IS ALWAYS SYMETRIC, but not necessarily positive-definite. If it is
>>  singular, we think this system to be unstable. Because of the symetry, I
>>  always use Cholesky Decompsition to reduce the size of [K]. However, now
>>  I have some situation that [K] is negative-definite but I still have to
>>  solve the equation. I have not try Gauss method yet, however.
>> 
>You could try the Bunch-Kaufmann method - see Golub + Van Loan, Matrix
>Computations Sec 4.4, 2nd edition, 1989 Software is available in LAPACK
>on netlib.

Another useful reference is: 
@book{Gill1981,
        title="Practical Optimization",
        author="Gill, Philip E. and Walter Murray and Margaret H. Wright",
        year=1981,
        publisher="Academic Press"}

It describes a modified Cholesky decomposition that attempts to
minimize the error due to ill-conditioning.

I didn't bring it home this weekend, so I can't type anything in on
this.

I'm not aware of the availability of SPECIFIC code for this, but
wouldn't be surprised if there's something floating around in FORTRAN.

I've got some C code by Ajay Shah that does normal Cholesky, but
that's probably not what you want :-(.

-- 
Christopher Browne                |     PGP 2.0 key available
cbbrowne@csi.uottawa.ca           |======================================
University of Ottawa              | Genius may have its limitations, but
Master of System Science Program  | stupidity is not thus handicapped.