@inproceedings{544c41a24533447c891f6fac43a47b31,
title = "Preconditioning for nonsymmetry and time-dependence",
abstract = "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.",
author = "Eleanor McDonald and Sean Hon and Jennifer Pestana and Andy Wathen",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG 2017.; 23rd International Conference on Domain Decomposition Methods, DD23 ; Conference date: 06-07-2015 Through 10-07-2015",
year = "2017",
month = mar,
day = "18",
doi = "10.1007/978-3-319-52389-7_7",
language = "English",
isbn = "9783319523880",
series = "Lecture Notes in Computational Science and Engineering",
publisher = "Springer Cham",
pages = "81--91",
editor = "Chang-Ock Lee and Xiao-Chuan Cai and Keyes, {David E.} and Kim, {Hyea Hyun} and Axel Klawonn and Eun-Jae Park and Widlund, {Olof B.}",
booktitle = "Domain Decomposition Methods in Science and Engineering XXIII",
edition = "1st",
}