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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 12, Pages 2092–2106 (Mi zvmmf64)  
This article is cited in 4 scientific papers (total in 4 papers)

A continuation method for solving symmetric Toeplitz systems

M. Van Barela, Kh. D. Ikramovb, A. A. Chesnokovba

a Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200 A, B-3001 Leuven, Belgium
b Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia
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Abstract: A fast algorithm is proposed for solving symmetric Toeplitz systems. This algorithm continuously transforms the identity matrix into the inverse of a given Toeplitz matrix $T$. The memory requirements for the algorithm are $O(n)$, and its complexity is $O(\log n k(T)n\log n)$, where $k(T)$ is the condition number of $T$. Numerical results are presented that confirm the efficiency of the proposed algorithm.
Key words: Toeplitz matrices, circulants, superfast algorithm, continuation method, iterative refinement, eigenvalues.
Received: 29.12.2007
Revised: 22.05.2008
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 12, Pages 2126–2139
DOI: https://doi.org/10.1134/S0965542508120026
Bibliographic databases:
Document Type: Article
UDC: 519.612
Language: Russian
Citation: M. Van Barel, Kh. D. Ikramov, A. A. Chesnokov, “A continuation method for solving symmetric Toeplitz systems”, Zh. Vychisl. Mat. Mat. Fiz., 48:12 (2008), 2092–2106; Comput. Math. Math. Phys., 48:12 (2008), 2126–2139
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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