A new algorithm for solving Toeplitz linear systems
| dc.citation.epage | 815 | |
| dc.citation.issue | 3 | |
| dc.citation.journalTitle | Математичне моделювання та комп'ютинг | |
| dc.citation.spage | 807 | |
| dc.contributor.affiliation | Університет Абдельмалек Ессааді | |
| dc.contributor.affiliation | Abdelmalek Essaadi University | |
| dc.contributor.author | Аулад, О. Ф. | |
| dc.contributor.author | Таяні, Ч. | |
| dc.contributor.author | Aoulad, O. F. | |
| dc.contributor.author | Tajani, C. | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2025-03-04T12:17:26Z | |
| dc.date.created | 2023-02-28 | |
| dc.date.issued | 2023-02-28 | |
| dc.description.abstract | У цій статті нас цікавить розв’язання лінійних систем Тепліца. Використовуючи спеціальну структуру Тепліца, даємо нову форму розкладання матриці коефіцієнтів. Базуючись на цій матричній формі декомпозиції та в поєднанні з формулою Шермана–Морісона, запропоновано ефективний алгоритм для розв’язання розглянутої проблеми. Наведено типовий приклад для ілюстрації різних кроків запропонованого алгоритму. Крім того, наведені чисельні тести, що демонструють ефективність нашого алгоритму. | |
| dc.description.abstract | In this paper, we are interested in solving the Toeplitz linear systems. By exploiting the special Toeplitz structure, we give a new decomposition form of the coefficient matrix. Based on this matrix decomposition form and combined with the Sherman–Morrison formula, we propose an efficient algorithm for solving the considered problem. A typical example is presented to illustrate the different steps of the proposed algorithm. In addition, numerical tests are given showing the efficiency of our algorithm. | |
| dc.format.extent | 807-815 | |
| dc.format.pages | 9 | |
| dc.identifier.citation | Aoulad O. F. A new algorithm for solving Toeplitz linear systems / O. F. Aoulad, C. Tajani // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 3. — P. 807–815. | |
| dc.identifier.citationen | Aoulad O. F. A new algorithm for solving Toeplitz linear systems / O. F. Aoulad, C. Tajani // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 3. — P. 807–815. | |
| dc.identifier.doi | doi.org/10.23939/mmc2023.03.807 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/63516 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Математичне моделювання та комп'ютинг, 3 (10), 2023 | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 3 (10), 2023 | |
| dc.relation.references | [1] Bunchy J. R. Stability of methods for solving Toeplitz systems of equations. SIAM Journal on Scientific Computing. 6 (2), 349–364 (1985). | |
| dc.relation.references | [2] Chesnakov A., Van Barel M. A direct method to solve block banded block Toeplitz systems with nonbanded Toeplitz block. Journal of Computational and Applied Mathematics. 234 (5), 1485–1491 (2010). | |
| dc.relation.references | [3] Bini D. Parallel solution of certain Toeplitz linear systems. SIAM Journal on Computing. 13 (2), 268–276 (1984). | |
| dc.relation.references | [4] Lin F.-R., Ching W.-K., Ng M. K. Fast inversion of triangular Toeplitz matrices. Theoretical Computer Science. 315 (2–3), 511–523 (2004). | |
| dc.relation.references | [5] Dongarra J. J., Moler C. B., Bunch J. R., Stewart G. W. LINPACK user’s guide. SIAM Press (1979). | |
| dc.relation.references | [6] Hockney R. W. A fast direct solution of Poisson’s equation using Fourier analysis. Journal of the ACM. 12 (1), 95–113 (1965). | |
| dc.relation.references | [7] Widlund O. B. On the use of fast methods for separable finite difference equations for the solution of general elliptic problems. In: Sparse matrices and their applications, Rose D. J., Willoughby R. A. (eds)). The IBM Research Symposia Series. Springer, Boston, MA. 121–131 (1972). | |
| dc.relation.references | [8] Malcolm M. A., Palmer J. A fast method for solving a class of tridiagonal linear systems. Communications of the ACM. 17 (1), 14–17 (1974). | |
| dc.relation.references | [9] Fischer D., Golub G., Hald O., Levia C., Widlund O. On Fourier–Toeplitz methods for separable elliptic problems. Mathematics of Computation. 28 (126), 349–368 (1974). | |
| dc.relation.references | [10] Rojo O. A new method for solving symmetric circulant tridiagonal systems of linear equations. Computers & Mathematics with Applications. 20 (12), 61–67 (1990). | |
| dc.relation.references | [11] Chen M. On the solution of circulant linear systems. SIAM Journal on Numerical Analysis. 24 (3), 668–683 (1987). | |
| dc.relation.references | [12] Belhaj S., Dridi M., Salam A. A fast algorithm for solving banded Toeplitz systems. Computers & Mathematics with Application. 70 (12), 2958–2967 (2015). | |
| dc.relation.referencesen | [1] Bunchy J. R. Stability of methods for solving Toeplitz systems of equations. SIAM Journal on Scientific Computing. 6 (2), 349–364 (1985). | |
| dc.relation.referencesen | [2] Chesnakov A., Van Barel M. A direct method to solve block banded block Toeplitz systems with nonbanded Toeplitz block. Journal of Computational and Applied Mathematics. 234 (5), 1485–1491 (2010). | |
| dc.relation.referencesen | [3] Bini D. Parallel solution of certain Toeplitz linear systems. SIAM Journal on Computing. 13 (2), 268–276 (1984). | |
| dc.relation.referencesen | [4] Lin F.-R., Ching W.-K., Ng M. K. Fast inversion of triangular Toeplitz matrices. Theoretical Computer Science. 315 (2–3), 511–523 (2004). | |
| dc.relation.referencesen | [5] Dongarra J. J., Moler C. B., Bunch J. R., Stewart G. W. LINPACK user’s guide. SIAM Press (1979). | |
| dc.relation.referencesen | [6] Hockney R. W. A fast direct solution of Poisson’s equation using Fourier analysis. Journal of the ACM. 12 (1), 95–113 (1965). | |
| dc.relation.referencesen | [7] Widlund O. B. On the use of fast methods for separable finite difference equations for the solution of general elliptic problems. In: Sparse matrices and their applications, Rose D. J., Willoughby R. A. (eds)). The IBM Research Symposia Series. Springer, Boston, MA. 121–131 (1972). | |
| dc.relation.referencesen | [8] Malcolm M. A., Palmer J. A fast method for solving a class of tridiagonal linear systems. Communications of the ACM. 17 (1), 14–17 (1974). | |
| dc.relation.referencesen | [9] Fischer D., Golub G., Hald O., Levia C., Widlund O. On Fourier–Toeplitz methods for separable elliptic problems. Mathematics of Computation. 28 (126), 349–368 (1974). | |
| dc.relation.referencesen | [10] Rojo O. A new method for solving symmetric circulant tridiagonal systems of linear equations. Computers & Mathematics with Applications. 20 (12), 61–67 (1990). | |
| dc.relation.referencesen | [11] Chen M. On the solution of circulant linear systems. SIAM Journal on Numerical Analysis. 24 (3), 668–683 (1987). | |
| dc.relation.referencesen | [12] Belhaj S., Dridi M., Salam A. A fast algorithm for solving banded Toeplitz systems. Computers & Mathematics with Application. 70 (12), 2958–2967 (2015). | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2023 | |
| dc.subject | матриця Тепліца | |
| dc.subject | формула Шермана–Морісона | |
| dc.subject | метод декомпозиціції | |
| dc.subject | Toeplitz matrix | |
| dc.subject | Sherman–Morrison formula | |
| dc.subject | decomposition method | |
| dc.title | A new algorithm for solving Toeplitz linear systems | |
| dc.title.alternative | Новий алгоритм розв’язування лінійних систем Тепліца | |
| dc.type | Article |
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