Schur Complement Preconditioners for Distributed General Sparse Linear Systems

This paper discusses the Schur complement viewpoint when developing parallel preconditioners for general sparse linear systems. Schur complement methods are pervasive in numerical linear algebra where they represent a canonical way of implementing divide-and-conquer principles. The goal of this note is to give a brief overview of recent progress made in using these techniques for solving general, irregularly structured, sparse linear systems. The emphasis is to point out the impact of Domain Decomposition ideas on the design of general purpose sparse system solution methods, as well as to show ideas that are of a purely algebraic nature.