Preconditioning for nonsymmetry and time-dependence

Eleanor McDonald, Sean Hon, Jennifer Pestana, Andrew Wathen

Research output: Contribution to conferenceProceeding

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.

Conference

Conference23rd International Conference on Domain Decomposition Methods
Abbreviated titleDD 23
CountryKorea, Democratic People's Republic of
CityJeju Island
Period6/07/1510/07/15

Fingerprint

Time Dependence
Preconditioning
Iteration
Normal Equations
Non-normality
Toeplitz matrix
Otto Toeplitz
Diagonal matrix
Preconditioner
Positive definite
Eigenvalue
Form

Keywords

  • preconditioning
  • nonsymmetric real Toeplitz matrices
  • Toeplitz matrix
  • time-dependence

Cite this

McDonald, E., Hon, S., Pestana, J., & Wathen, A. (2016). Preconditioning for nonsymmetry and time-dependence. 1-11. 23rd International Conference on Domain Decomposition Methods, Jeju Island, Korea, Democratic People's Republic of.
McDonald, Eleanor ; Hon, Sean ; Pestana, Jennifer ; Wathen, Andrew. / Preconditioning for nonsymmetry and time-dependence. 23rd International Conference on Domain Decomposition Methods, Jeju Island, Korea, Democratic People's Republic of.11 p.
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note = "23rd International Conference on Domain Decomposition Methods, DD 23 ; Conference date: 06-07-2015 Through 10-07-2015",

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McDonald, E, Hon, S, Pestana, J & Wathen, A 2016, 'Preconditioning for nonsymmetry and time-dependence' 23rd International Conference on Domain Decomposition Methods, Jeju Island, Korea, Democratic People's Republic of, 6/07/15 - 10/07/15, pp. 1-11.

Preconditioning for nonsymmetry and time-dependence. / McDonald, Eleanor; Hon, Sean; Pestana, Jennifer; Wathen, Andrew.

2016. 1-11 23rd International Conference on Domain Decomposition Methods, Jeju Island, Korea, Democratic People's Republic of.

Research output: Contribution to conferenceProceeding

TY - CONF

T1 - Preconditioning for nonsymmetry and time-dependence

AU - McDonald, Eleanor

AU - Hon, Sean

AU - Pestana, Jennifer

AU - Wathen, Andrew

PY - 2016/4/14

Y1 - 2016/4/14

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/

M3 - Proceeding

SP - 1

EP - 11

ER -

McDonald E, Hon S, Pestana J, Wathen A. Preconditioning for nonsymmetry and time-dependence. 2016. 23rd International Conference on Domain Decomposition Methods, Jeju Island, Korea, Democratic People's Republic of.