Skip to main content
Article thumbnail
Location of Repository

Preconditioners based on strong subgraphs

By Iain S. Duff and Kamer Kaya

Abstract

This paper proposes an approach for obtaining block diagonal and block triangular preconditioners that can be used for solving a linear system Ax = b, where A is a large, nonsingular, real, n × n sparse matrix. The proposed approach uses Tarjan’s algorithm for hierarchically decomposing a digraph into its strong subgraphs. To the best of our knowledge, this is the first work that uses this algorithm for preconditioning purposes. We describe the method, analyse its performance, and compare it with preconditioners from the literature such as ILUT and XPABLO and show that it is highly competitive with them in terms of both memory and iteration count. In addition, our approach shares with XPABLO the benefit of being able to exploit parallelism through a version that uses a block diagonal preconditioner

Topics: sparse matrices, strong subgraphs, strong components, preconditioners
Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.414.9833
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://www.cerfacs.fr/algor/re... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.