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A multicore solution to Block–Toeplitz linear systems of equations

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Abstract

There exist algorithms, also called “fast” algorithms, which exploit the special structure of Toeplitz matrices so that, e.g., allow to solve a linear system of equations in O(n 2) flops. However, some implementations of classical algorithms that do not use this structure (O(n 3) flops) highly reduce the time to solution when several cores are available. That is why it is necessary to work on “fast” algorithms so that they do not lose track of the benefits of new hardware/software. In this work, we propose a new approach to the Generalized Schur Algorithm, a very known algorithm for the solution of Toeplitz systems, to work on a Block–Toeplitz matrix. Our algorithm is based on matrix–matrix multiplications, thus allowing to exploit an efficient implementation of this operation if it exists. Our algorithm also makes use of the thread level parallelism featured by multicores to decrease execution time.

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Acknowledgements

PROMETEO/2009/013, Generalitat Valenciana. Projects TEC2009-13741, TIN2010-14971 and TIN2011-15734-E of the Ministerio Español de Ciencia e Innovación, and TEC2012-38142-C04 of the Ministerio Español de Economía y Competitividad.

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Authors and Affiliations

  1. Departamento de Sistemas Informáticos y Computación, Universitat Politècnica de València, València, Spain

    Pedro Alonso & Antonio M. Vidal

  2. Departamento de Informática, Universidad de Oviedo, Gijón, Spain

    Daniel Argüelles & José Ranilla

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  1. Pedro Alonso
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  2. Daniel Argüelles
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  3. José Ranilla
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  4. Antonio M. Vidal
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Correspondence to Pedro Alonso.

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Alonso, P., Argüelles, D., Ranilla, J. et al. A multicore solution to Block–Toeplitz linear systems of equations. J Supercomput 65, 999–1009 (2013). https://doi.org/10.1007/s11227-012-0824-4

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