Sparse Cholesky is an algorithm for solving a linear system of equations
where
is sparse and symmetric positive definite. It is
basically LU factorization, where positive definiteness means that
,
and any pivot order can be used.
There are a number of complicated data structures involved to exploit the
sparsity and ensure that
a minimum amount of storage and minimal floating point operations are performed.
There are a number of ways to layout data, and detect and schedule
parallelism. Only recently have reasonable speedups been attained for this
problem. We have a pretty good parallel implementation for which we have
a number of optimizations that could be implemented and measured.
I expect this could be a very good implementation if the optimizations
are successful.