Efficient ways to solve sparse linear systems

Hello! I’m new at CUDA and espesially at cuSparse, so I need your advice.

I’m studying sparse linear systems and want to find out different methods to solve them. I’ve already tried to use conjugate gradient from cusp library with its method cusp::krylov::cg. That’s ok.
The question is about cuSparse. I found out that there’s a function csric0 which factorizes matrix A: A = Rt*R, where R is a triangular matrix. I tried to use this factorization and function which solves triangular systems this way: Ax=b => Rt * R * x = b
=> Rt * y = b and R * x = y.
But finally I got x approximately. As I understand this decomposition is actually the Cholesky decomposition, but factorization with csric0 is approximate and that’s why it is inappropriate here. Is csric0 used only for preconditioners?

My question is what are other ways to solve sparse systems using cuSparse? For example, is it possible to find exact solution using Cholesky decomposition?