Alonso-Jordá, P.; Dolz Zaragozá, MF.; Vidal Maciá, AM. (2014). Block pivoting implementation of a symmetric Toeplitz solver. Journal of Parallel and Distributed Computing. 74(5):2392-2399. doi:10.1016/j.jpdc.2014.02.003
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/57022
Title:
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Block pivoting implementation of a symmetric Toeplitz solver
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Author:
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Alonso-Jordá, Pedro
Dolz Zaragozá, Manuel Francisco
Vidal Maciá, Antonio Manuel
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UPV Unit:
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Universitat Politècnica de València. Departamento de Sistemas Informáticos y Computación - Departament de Sistemes Informàtics i Computació
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Issued date:
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Abstract:
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Toeplitz matrices are characterized by a special structure that can be exploited in order to obtain fast linear system solvers. These solvers are difficult to parallelize due to their low computational cost and their closely ...[+]
Toeplitz matrices are characterized by a special structure that can be exploited in order to obtain fast linear system solvers. These solvers are difficult to parallelize due to their low computational cost and their closely coupled data operations. We propose to transform the Toeplitz system matrix into a Cauchy-like matrix since the latter can be divided into two independent matrices of half the size of the system matrix and each one of these smaller arising matrices can be factorized efficiently in multicore computers. We use OpenMP and store data in memory by blocks in consecutive positions yielding a simple and efficient algorithm. In addition, by exploiting the fact that diagonal pivoting does not destroy the special structure of Cauchy-like matrices, we introduce a local diagonal pivoting technique which improves the accuracy of the solution and the stability of the algorithm.
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Subjects:
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Symmetric Toeplitz matrices
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Linear systems
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Pivoting
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Displacement structure
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Multicores
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Copyrigths:
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Reserva de todos los derechos
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Source:
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Journal of Parallel and Distributed Computing. (issn:
0743-7315
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DOI:
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10.1016/j.jpdc.2014.02.003
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Publisher:
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Elsevier
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Publisher version:
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http://dx.doi.org/10.1016/j.jpdc.2014.02.003
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Project ID:
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MICINN/TIN2008-06570-C04-02
MICINN/TEC2009-13741
UPV/PAID-05-10 (ref. 2705)
GVA/PROMETEO/2009/2013
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Thanks:
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This work was partially supported by the Spanish Ministerio de Ciencia e Innovacion (Project TIN2008-06570-C04-02 and TEC2009-13741), Vicerrectorado de Investigacion de la Universidad Politecnica de Valencia through ...[+]
This work was partially supported by the Spanish Ministerio de Ciencia e Innovacion (Project TIN2008-06570-C04-02 and TEC2009-13741), Vicerrectorado de Investigacion de la Universidad Politecnica de Valencia through PAID-05-10 (ref. 2705), and Generalitat Valenciana through project PROMETEO/2009/2013.
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Type:
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Artículo
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