Sparse Cholesky.

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.