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Title: | An evaluation of four reordering algorithms to reduce the computational cost of the Jacobi-preconditioned conjugate gradient method using high-precision arithmetic |
Keywords: | Bandwidth reduction Self-organising maps Conjugate gradient method Combinatorial optimisation Redução de largura de banda Mapas auto-organizados Método do gradiente conjugado Otimização combinatória |
Issue Date: | 2017 |
Publisher: | Inderscience Enterprises |
Citation: | OLIVEIRA, S. L. G. de; ABREU, A. A. A. M. de; ROBAINA, D.; KISCHINHEVSKY, M. An evaluation of four reordering algorithms to reduce the computational cost of the Jacobi-preconditioned conjugate gradient method using high-precision arithmetic. International Journal of Business Intelligence and Data Mining, [S. l.], v. 12, n. 2, 2017. DOI: https://doi.org/10.1504/IJBIDM.2017.084281. |
Abstract: | In this work, four heuristics for bandwidth and profile reductions are evaluated. Specifically, the results of a recent proposed heuristic for bandwidth and profile reductions of symmetric and asymmetric matrices using a one-dimensional self-organising map is evaluated against the results obtained from the variable neighbourhood search for bandwidth reduction heuristic, the original reverse Cuthill-McKee method, and the reverse Cuthill-McKee method with starting pseudo-peripheral vertex given by the George-Liu algorithm. These four heuristics were applied to three datasets of linear systems composed of sparse symmetric positive-definite matrices arising from discretisations of the heat conduction and Laplace equations by finite volumes. The linear systems are solved by the Jacobi-preconditioned conjugate gradient method when using high-precision numerical computations. The best heuristic in the simulations performed with one of the datasets used was the Cuthill-McKee method with starting pseudo-peripheral vertex given by the George-Liu algorithm. On the other hand, no gain was obtained in relation to the computational cost of the linear system solver when a heuristic for bandwidth and profile reduction is applied to instances contained in two of the datasets used. |
URI: | https://www.inderscienceonline.com/doi/abs/10.1504/IJBIDM.2017.084281 http://repositorio.ufla.br/jspui/handle/1/36671 |
Appears in Collections: | DCC - Artigos publicados em periódicos |
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