A comparative study of null‐space factorizations for sparse symmetric saddle point systems. Issue 1 (6th June 2017)

• Record Type: Journal Article
• Authors: Rees, Tyrone; Scott, Jennifer
• Is Part Of: Numerical linear algebra with applications. Volume 25:Issue 1(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2017-06-06
• Subjects: direct methods, null‐space methods, saddle point systems, sparse symmetric indefinite systems; Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.2103
• Languages: English
• ISSNs: 1070-5325

Abstract

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.