Hi folks, I have a matrix as a result of a finite element discretization of the Poisson operator and associated right hand side. As it turns out, the matrix is symmetric but not positive definite since it has at least two negative small eigenvalues. I have been solving this system without problem using the conjugate gradients (CG) algorithm with ML as a preconditioner, but I'm wondering why it works.
Shouldn't CG fail for a non-positive-definite matrix? Does PETSc do some additional magic if it detects that the dot-product in the CG algorithm is negative? Does it solve the system using the normal equations, A'A, instead? Please let me know if I should send the matrix + rhs. Thanks, Jozsef
