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https://hdl.handle.net/123456789/1541| Τύπος: | Πρακτικά συνεδρίου |
| Τίτλος: | Band preconditioners for non-symmetric real Toeplitz systems with unknown generating function |
| Συγγραφέας: | [EL] Σάισι, Τάνιπον[EN] Chaysri, Thaniporn [EL] Χατζηδήμος, Απόστολος[EN] Hadjidimos, Apostolos [EL] Νούτσος, Δημήτριος[EN] Noutsos, Dimitrios [EL] Ταχυρίδης, Γρηγόριος[EN] Tachyridis, Grigorios |
| Ημερομηνία: | Ιου-2021 |
| Περίληψη: | Toeplitz systems appear in a variety of applications in real life such as signal processing, image processing and restoration and discretization of PDEs. The fast convergence to the accurate solution of the system seems to be necessary, taking into account that the dimension of the arising systems is very large. It is well known that iterative methods and especially Krylov subspace methods are the most efficient methods for this kind of problems. Toeplitz matrices are generated by 2π-periodic generating functions. In many applications the generating function has roots at some points and this is transferred to the Toeplitz matrix, which becomes ill-conditioned. As it is widely known, this can be overcome by using an appropriate preconditioner. Symmetric and positive definite Toeplitz systems were extensively studied by many researchers. Real, non-symmetric and positive definite or non-definite Toeplitz systems also appear in applications and attract the interest of researchers. In some problems the generating function is not known a priori.In this paper, we study a preconditioning technique for non-symmetric, real Toeplitz systems with unknown generating function. We focus on ill-conditioned systems of such form and we aim to present extensively the band Toeplitz preconditioner’s construction procedure by the entries of the initial system. From the entries of the coefficient matrix T n we estimate the unknown function, forming its Fourier expansion, on an equally spaced grid G n in (−π, π). Then, we propose a procedure to estimate possible roots of the generating function and their multiplicities, in order to form the trigonometric polynomial that eliminates the roots. After eliminating the roots, we apply the well-known Remez algorithm for further approximation. An algorithm describing step-by-step this procedure is presented. Theoretical results concerning the spectra clustering are also given. Suitable numerical examples are demonstrated to show the validity and efficiency of the proposed preconditioning technique, using the Preconditioned Generalized Minimal Residual method (PGMRES). |
| Γλώσσα: | Αγγλικά |
| Σελίδες: | 10 |
| DOI: | 10.1109/CSCC53858.2021.00024 |
| ISBN: | 978-1-6654-2749-4 |
| Θεματική κατηγορία: | [EL] Εφαρμοσμένα μαθηματικά[EN] Applied Mathematics |
| Λέξεις-κλειδιά: | Non-symmetric matrices; Clustering; Preconditioning; Toeplitz |
| Κάτοχος πνευματικών δικαιωμάτων: | © 2021 by the Institute of Electrical and Electronics Engineers, Inc. All Rights Reserved |
| Όροι και προϋποθέσεις δικαιωμάτων: | Abstracting is permitted with credit to the source. Libraries are permitted to photocopy beyond the limit of U.S. copyright law for private use of patrons those articles in this volume that carry a code at the bottom of the first page, provided the per-copy fee indicated in the code is paid through Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923. For other copying, reprint or republication permission, write to IEEE Copyrights Manager, IEEE Service Center, 445 Hoes Lane, Piscataway, NJ 08854. All rights reserved. |
| Ηλεκτρονική διεύθυνση του τεκμηρίου στον εκδότη: | https://ieeexplore.ieee.org/document/9668725 |
| Ηλεκτρονική διεύθυνση περιοδικού: | https://ieeexplore.ieee.org/xpl/conhome/9668309/proceeding |
| Τίτλος πηγής δημοσίευσης: | 2021 Proceedings of the 25th International Conference on Circuits, Systems, Communications and Computers (CSCC) |
| Σελίδες τεκμηρίου (στην πηγή): | 86-96 |
| Όνομα εκδήλωσης: | 25th International Conference on Circuits, Systems, Communications and Computers (CSCC) |
| Τοποθεσία εκδήλωσης: | Crete island, Greece |
| Ημ/νία έναρξης εκδήλωσης: | 19/07/2021 |
| Ημ/νία λήξης εκδήλωσης: | 22/07/2021 |
| Σημειώσεις: | This research is co-financed by Greece and the European Union (European Social Fund-ESF) through the Operational Programme Human Resources Development, Education and Lifelong Learning 2014-2020 in the context of the project “Krylov subspace methods and Perron-Frobenius theory” (MIS 5047643). |
| Εμφανίζεται στις συλλογές: | Ερευνητικές ομάδες |
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