Hi! I’m trying to find the smallest singular vector of a sparse (16900x16900) Hermitian BigFloat
matrix A. Is there a standard way to do this?
My current idea is to use ArnoldiMethod.partialschur with a function that applies the inverse of A. To get this function, I would first find a sparse LU decomposition of A ( with IncompleteLU.jl, following this guy ), then apply one of the IterativeSolvers functions (like conjugate gradients??). Would that work?
(Another question is, if the original matrix has a 1d kernel, how can I find the kernel?)
I am not very familiar with how any of the linear algebra algorithms work (maybe I should learn), but I just want my eigenvector. Any help would be greatly appreciated! Thanks!