I have a large system of equations
and I know matrix $A$ and right-hand side vector $b$. I'm using MKL to solve this system. The matrices are complex. I have used the general solver
(Intel MKL zgetrs) which needs the matrix input in LU decomposition. So I have used
ZGETRF (Intel MKL zgetrf) that performs the LU decomposition.
I checked the matrix $A$ through SVD as well - the SVD decomposition says no problem, matrix $A$ is regular.
But when I send the $A$ to
ZGETRF, there comes a error code "4" (from manual if
info is positive, "The factorization has been completed, but $U$ is exactly singular. Division by 0 will occur if you use the factor $U$ for solving a system of linear equations.")
But then the program send the LU-factorized matrix $A$ to
ZGETRS, which should solve the $Ax=b$ system. And this one writes me no error (
But the solution it gives me is trivial solution - all unknouwns should be zero.
What does it mean - where could be the error in the matrix? When SVD says the matrix is regular but LU decomposer says it's singular?