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EnglishThe normal equations constructed by a Toeplitz matrix are studied, in order to find a suitable preconditioner related to the discrete sine transform. New results are given about the structure of the product of two Toeplitz matrices, which allow the CGN method to achieve a superlinear rate of convergence. This preconditioner outperforms the circulant one for the iterative solution of Toeplitz least-squares problems; such strategy can also be applied to nonsymmetric linear systems. A block generalization is discussed.
Solution of Toeplitz normal equations by sine transform based preconditioning / F. DI BENEDETTO. - In: LINEAR ALGEBRA AND ITS APPLICATIONS. - ISSN 0024-3795. - STAMPA. - 285(1998), pp. 229-255.
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| Titolo: | Solution of Toeplitz normal equations by sine transform based preconditioning |
| Autori: | |
| Data di pubblicazione: | 1998 |
| Rivista: | |
| Citazione: | Solution of Toeplitz normal equations by sine transform based preconditioning / F. DI BENEDETTO. - In: LINEAR ALGEBRA AND ITS APPLICATIONS. - ISSN 0024-3795. - STAMPA. - 285(1998), pp. 229-255. |
| Abstract: | The normal equations constructed by a Toeplitz matrix are studied, in order to find a suitable preconditioner related to the discrete sine transform. New results are given about the structure of the product of two Toeplitz matrices, which allow the CGN method to achieve a superlinear rate of convergence. This preconditioner outperforms the circulant one for the iterative solution of Toeplitz least-squares problems; such strategy can also be applied to nonsymmetric linear systems. A block generalization is discussed. |
| Handle: | http://hdl.handle.net/11567/193044 |
| Appare nelle tipologie: | 01.01 - Articolo su rivista |
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