A comparative study of null‐space factorizations for sparse symmetric saddle point systems. Issue 1 (6th June 2017) - Rees, Tyrone; Scott, Jennifer
Summary: Null‐space methods for solving saddle point systems of equations have long been used to transform an indefinite system into a symmetric positive definite one of smaller dimension. A number of independent works in the literature have identified that we can interpret a null‐space method as a matrix factorization. We review these findings, highlight links between them, and bring them into a unified framework. We also investigate the suitability of using null‐space factorizations to derive sparse direct methods and present numerical results for both practical and academic problems.