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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 (before 2015) Signal Processing Laboratory
Indexed by ISI Yes


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.