Best generic method to solve homogeneous system

General Usage
1

What is the best way to solve the homogeneous system A\vec{x}=\vec{0} for either a dense or sparse array (or even GPU array)?

For dense A, nullspace(A) works, and for a sparse array, eigs(A,nev=1,which=:SM) appears to work fine.

Is there a better, generic, method somewhere? I looked at IterativeSolvers with b=\vec{0}, but that doesn’t seem to return the right answer.

2

Note that until now, I had been using NLsolve, but that seems quite wasteful considering that the lu factorization is needlessly recomputed at each step.

3

One simple answer is to compete and store the lu factorization.

4

With NLsolve? How would that work?