I'm trying to solve
$Ax = b$
given a vector $b$ and a large, symmetric positive definite, sparse, banded matrix $A$ that has a very poor condition number.
I know several iterative methods that could be used for this task (but haven't implemented them all):
a) (Preconditioned) Conjugate Gradient.
b) Simple Gradient Descent.
c) SSOR / Gauss-Seidel.
d) Multigrid flavors of the above.
Also, I know that there are sparse direct solvers but I have been reluctant to try because they seem very complex and hard to implement.
So what's the method of choice here?