Norm-Coarsened Ordering for Parallel Incomplete Cholesky Preconditioning

The ordering of a matrix vastly impact the convergence rate of precondition conjugate gradient method. Past ordering methods focus solely on a graph representation of the sparse matrix and do not give an inside into the convergence rate that is linked to the preconditioned eigenspectrum. This work attempt to investigate how numerical based ordering may produce a better preconditioned system in terms of faster convergence.