🚀 go-pugleaf

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.
>    Does anyone kow :
>    1) Is there any method I can use to reduce [K], and still solve the system
>       when [K] is negative-definite ? (Note that [K] IS ALWAYS SYMETRIC)
>    2) If such method exists, what's the criteria for positive- or negative-
>       definite?
>    3) If no such method exits,( We can not take advantage of symetry to
>       reduce the size of [k], I mean.), does Gauss method work? What's
>       the criteria for question (2)?
> 
>  NOTE : (1) In such system, we do not do pivotting among the rows of [K],
>             if using Gauss method. If there is a zero on the diagonal,
>             we consider it as unstable.
You will have to pivot.
>         (2)      [ ] ====> matrix      { } ====> column vector
> 
>    It will be greatly appreciated if anyone can give me some idea. If you
>  do not want to type all that stuff to me, just tell me the theorem used.
>  Of course, it will be better if you can tell me reference books. Any
>  assistance will be greatly appreciated.
> 
>    Thank you very very very much !!!!!!
Richard.
-- 
** R.W. Brankin -- Numerical Algorithms Group Ltd. -- nagrwb@vax.ox.ac.uk **
**   suggestions for sig. welcome   --   will need   include<std.discl>   **