Direct and Incomplete Cholesky Factorizations with Static Supernodes
Incomplete factorizations of sparse symmetric positive definite (SSPD) matrices have been used to generate preconditioners for various iterative solvers. These solvers generally use preconditioners derived from the matrix system, in order to reduce the total number of iterations until convergence. In this report, we investigate the findings of ref. [1] on their method for computing preconditioners from SSPD matrix. In particular, we focus on their supernodal Cholesky factorization algorithm designed for matrices with naturally occurring block structures.
Reference:
[1] Adaptive Techniques for Improving the Performance of Incomplete Factorization Preconditioning. Anshul Gupta and Thomas George, SIAM, February 8, 2010.