Preconditioning for nonsymmetry and time-dependence

Eleanor McDonald*, Sean Hon, Jennifer Pestana, Andy Wathen

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingConference proceedingpeer-review

8 Citations (Scopus)


For symmetric systems, rigorous convergence bounds can be obtained which depend only on the eigenvalues of the system. However for nonsymmetric systems, no generally descriptive convergence bounds are known and therefore the development of preconditioners for these problems is typically heuristic. In this paper, we describe one simple but frequently occurring example of nonsymmetric Toeplitz matrices, where we are able to guarantee rapid convergence of an appropriate iterative method. The method employs a simple trick of reordering the variables to rewrite the system as a symmetric one. A symmetric positive definite absolute value preconditioner is also proposed which is used within a standard symmetric solver such as minres. We also show how this can be applied to time-dependent linear ODEs which are inherently nonsymmetric.

Original languageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XXIII
EditorsChang-Ock Lee, Xiao-Chuan Cai, David E. Keyes, Hyea Hyun Kim, Axel Klawonn, Eun-Jae Park, Olof B. Widlund
PublisherSpringer Cham
Number of pages11
ISBN (Electronic)9783319523897
ISBN (Print)9783319523880, 9783319848945
Publication statusPublished - 18 Mar 2017
Event23rd International Conference on Domain Decomposition Methods, DD23 - Jeju Island, Korea, Republic of
Duration: 6 Jul 201510 Jul 2015

Publication series

NameLecture Notes in Computational Science and Engineering
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100


Conference23rd International Conference on Domain Decomposition Methods, DD23
Country/TerritoryKorea, Republic of
City Jeju Island

Scopus Subject Areas

  • Modelling and Simulation
  • Engineering(all)
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics


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