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.
|Number of pages||11|
|Publication status||Published - 14 Apr 2016|
|Event||23rd International Conference on Domain Decomposition Methods - Jeju Island, Korea, Democratic People's Republic of|
Duration: 6 Jul 2015 → 10 Jul 2015
|Conference||23rd International Conference on Domain Decomposition Methods|
|Abbreviated title||DD 23|
|Country||Korea, Democratic People's Republic of|
|Period||6/07/15 → 10/07/15|
- nonsymmetric real Toeplitz matrices
- Toeplitz matrix
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.