From: Stefan Jahn <stefan@gr...>  20071229 12:59:52

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 pivotstrategy give slightly different results due to numerical errors Thus the question is: Is there a preconditionmethod 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 pivotstrategy is used. Hope this is a question in fact, Stefan. 