Abstract
A parallel algorithm for solving complex hermitian Toeplitz linear systems is presented. The parallel algorithm exploits the special structure of Toeplitz matrices to obtain the solution in a quadratic asymptotical cost. Our parallel algorithm transfors the Toeplitz matrix into a Cauchy–like matrix. Working on a Cauchy–like system lets to work with real arithmetic. The parallel algorithm for the solution of a Cauchy–like matrix has a low amount of communication cost regarding other parallel algorithms that work directly on the Toeplitz system. We use a message–passing programming model. The experimental tests are obtained in a cluster of personal computers.
Supported by Spanish MCYT and FEDER under Grant TIC 2003-08238-C02-02.
Funded by Secretaría de Estado de Universidades e Investigación del Ministerio de Educación y Cultura of Spain.
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Alonso, P., Bernabeu, M.O., Vidal, A.M. (2006). A Parallel Solution of Hermitian Toeplitz Linear Systems,. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science – ICCS 2006. ICCS 2006. Lecture Notes in Computer Science, vol 3991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11758501_49
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