Firstly, hello everyone!

I am loïc, a french student (so please be kind with my **** english) in fluid mechanics.

In the context of a 6 months project i am developping in C++ a code allowing users to simulate a flow around an airfoil profile.
In this code, I need to solve big linear systems (A*X=B), with A being a large float matrix (up to 1000*1000 and beyond!) and B a column vector.

I came across Eigen, which seemed the best choice for solving such systems, and seemed to work pretty well.

BUT, I am encountering difficulties right now:
The various decompositions offered by Eigen give me different results (and not a little different, I mean resuts seem to live and behave on independant planets ).
My matrix being quite a messy one (no zeros, positive and negative members, no symetry...etc.), I used:

*FullPivLU: This one seemed the best, giving me results which could be realistic, but not as much as they should have.
*HouseholderQR: Quite worse, the results could be realistic, but on a strange world populated with funny creatures.
*ColPivHouseholderQR: Not the worst one, but irrealistic results.
*FullPivHouseholderQR : Doesn't even cares about giving me any result .

My question(s):
-How is this possible? I have no PHD in mathematics but studied linear algebra a (little) lot, and even if the methods are different, the results should not change that much right?
-Is this a known problem, and has anyone experienced it before?
-If so, are there any hints on how to process (validating the results, and maybe having the same results with the different methods)?

As you might feel I'm a little lost right there, so any help would really be appreciated. I could post a simple version of my code later if needed.
Thanks in advance to everyone (anyone)!
Eigenly yours,
Loïc.

Hi,

it might likely be the case that your problem very hill conditioned, and that applying a simple scaling would solve all your problems. If you can share a simple code to reproduce the issue might help. You might also print the column norms:

std::cout << A.colwise().norm() << "\n";

and singular values:

std::cout << A.jacobiSvd().singularValues().transpose() << "\n";

and report them.