Re: [Qucs-help] Same schematic, different results

[Stefan J. <st...@gr...>]

Am Sa, 29.12.2007, 13:27, schrieb Bastien ROUCARIES:

Hello!

> In fact I know a world class specialist of precondionning and inversion
> problem. He is sitting in the building near me at uni. I will try to talk
> to
> him about the problem.
>
> Could you give me some pointer to documentation? He is a pure math guy, so
> in
> order to have a quick and efficient tip, we need to ask him a mathematical
> question. THerefore could you explain fully the problem?

It is something like this:

 * equation systems can be solved with different solvers (e.g. LU, QR,
   SVD, inversion, etc.)
 * the given matrix and right hand side can be modified (exchanging
   columns or rows) without chaning the euqation system
 * during some of the solution algorithms pivoting is used; this leaves
   also a degree of freedom (pivot element can be choosen)
 * the method, matrix order as well as the pivot-strategy give
   slightly different results due to numerical errors

Thus the question is:

Is there a precondition-method which allows a solver to solve the
equation system more accurate (even for almost singular matrices).
I think a precondition always must consider which solver/decomposer
is used and also which pivot-strategy is used.

Hope this is a question in fact,
  Stefan.