Preconditioners for ill‐posed Toeplitz matrices with differentiable generating functions |
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Authors: | C Estatico |
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Institution: | 1. Dipartimento di Matematica e Informatica, Università di Cagliari, Via Ospedale 72, 09124 Cagliari, Italy;2. Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy |
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Abstract: | Both theoretical analysis and numerical experiments in the literature have shown that the Tyrtyshnikov circulant superoptimal preconditioner for Toeplitz systems can speed up the convergence of iterative methods without amplifying the noise of the data. Here we study a family of Tyrtyshnikov‐based preconditioners for discrete ill‐posed Toeplitz systems with differentiable generating functions. In particular, we show that the distribution of the eigenvalues of these preconditioners has good regularization features, since the smallest eigenvalues stay well separated from zero. Some numerical results confirm the regularization effectiveness of this family of preconditioners. Copyright © 2009 John Wiley & Sons, Ltd. |
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Keywords: | preconditioning ill‐determined rank iterative regularization Toeplitz matrices generating function |
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