Dominguez-Jimenez-2009a
From IEETA
Article
| Title | A New Preconditioner for Toeplitz Matrices |
|---|---|
| Author | M. Elena Domínguez-Jiménez, Paulo J S G Ferreira |
| Journal | IEEE Signal Processing Letters |
| Volume | 16 |
| Number | 9 |
| Pages | 758-761 |
| Month | September |
| Year | 2009 |
| DOI | doi:10.1109/LSP.2009.2024735 |
| Group | |
| Group (before 2015) | Signal Processing Laboratory |
| Indexed by ISI | Yes |
Abstract
This paper introduces and analyzes a new preconditioner for Toeplitz matrices that exhibits excellent spectral properties: the eigenvalues of the preconditioned matrix are highly clustered around the unity. When used with the preconditioned conjugate gradient method this results in very fast convergence. The new preconditioner can be regarded as a refinement of preconditioners built by embedding the Toeplitz matrix in a positive definite circulant. Necessary and sufficient conditions that ensure that the positive definite embedding is possible are given.