Preconditioning for nonsymmetry and time-dependence

Eleanor McDonald; Sean Hon; Jennifer Pestana; Andrew Wathen

doi:10.1007/978-3-319-52389-7_7

Preconditioning for nonsymmetry and time-dependence

Eleanor McDonald, Sean Hon, Jennifer Pestana, Andrew Wathen

Mathematics And Statistics

Research output: Contribution to conference › Proceeding › peer-review

17 Citations (Scopus)

92 Downloads (Pure)

Abstract

In this short paper, we decribe at least one simple and frequently arising situation |that of nonsymmetric real Toeplitz (constant diagonal) matrices| where we can guarantee rapid convergence of the appropriate iterative method by manipulating the problem into a symmetric form without recourse to the normal equations. This trick can be applied regardless of the nonnormality of the Toeplitz matrix. We also propose a symmetric and positive definite preconditioner for this situation which is proved to cluster eigenvalues and is by consequence guaranteed to ensure convergence in a number of iterations independent of the matrix dimension.

Original language	English
Pages	1-11
Number of pages	11
DOIs	https://doi.org/10.1007/978-3-319-52389-7_7
Publication status	Published - 18 Mar 2017
Event	23rd International Conference on Domain Decomposition Methods - Jeju Island, Korea, Democratic People's Republic of Duration: 6 Jul 2015 → 10 Jul 2015

Conference

Conference	23rd International Conference on Domain Decomposition Methods
Abbreviated title	DD 23
Country/Territory	Korea, Democratic People's Republic of
City	Jeju Island
Period	6/07/15 → 10/07/15

Keywords

preconditioning
nonsymmetric real Toeplitz matrices
Toeplitz matrix
time-dependence

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10.1007/978-3-319-52389-7_7

McDonald-etal-DD2015-preconditioning-nonsymmetry-time-dependenceAccepted author manuscript, 301 KB

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T1 - Preconditioning for nonsymmetry and time-dependence

AU - McDonald, Eleanor

AU - Hon, Sean

AU - Pestana, Jennifer

AU - Wathen, Andrew

PY - 2017/3/18

Y1 - 2017/3/18

N2 - In this short paper, we decribe at least one simple and frequently arising situation |that of nonsymmetric real Toeplitz (constant diagonal) matrices| where we can guarantee rapid convergence of the appropriate iterative method by manipulating the problem into a symmetric form without recourse to the normal equations. This trick can be applied regardless of the nonnormality of the Toeplitz matrix. We also propose a symmetric and positive definite preconditioner for this situation which is proved to cluster eigenvalues and is by consequence guaranteed to ensure convergence in a number of iterations independent of the matrix dimension.

AB - In this short paper, we decribe at least one simple and frequently arising situation |that of nonsymmetric real Toeplitz (constant diagonal) matrices| where we can guarantee rapid convergence of the appropriate iterative method by manipulating the problem into a symmetric form without recourse to the normal equations. This trick can be applied regardless of the nonnormality of the Toeplitz matrix. We also propose a symmetric and positive definite preconditioner for this situation which is proved to cluster eigenvalues and is by consequence guaranteed to ensure convergence in a number of iterations independent of the matrix dimension.

KW - preconditioning

KW - nonsymmetric real Toeplitz matrices

KW - Toeplitz matrix

KW - time-dependence

UR - http://dd23.kaist.ac.kr/

U2 - 10.1007/978-3-319-52389-7_7

DO - 10.1007/978-3-319-52389-7_7

M3 - Proceeding

SP - 1

EP - 11

T2 - 23rd International Conference on Domain Decomposition Methods

Y2 - 6 July 2015 through 10 July 2015

ER -

Preconditioning for nonsymmetry and time-dependence

Abstract

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Keywords

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