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An Analysis of Reordering Algorithms to Reduce the Computational Cost of the Jacobi-Preconditioned CG Solver Using High-Precision Arithmetic

2017; Springer Science+Business Media; Linguagem: Inglês

10.1007/978-3-319-62392-4_1

1611-3349

Sanderson L. Gonzaga de Oliveira, Guilherme Oliveira Chagas, Júnior Assis Barreto Bernardes,

Advanced Numerical Methods in Computational Mathematics

Several heuristics for bandwidth and profile reductions have been proposed since the 1960s. In systematic reviews, 133 heuristics applied to these problems have been found. The results of these heuristics have been analyzed so that, among them, 13 were selected in a manner that no simulation or comparison showed that these algorithms could be outperformed by any other algorithm in the publications analyzed, in terms of bandwidth or profile reductions and also considering the computational costs of the heuristics. Therefore, these 13 heuristics were selected as the most promising low-cost methods to solve these problems. Based on this experience, this article reports that in certain cases no heuristic for bandwidth or profile reduction can reduce the computational cost of the Jacobi-preconditioned Conjugate Gradient Method when using high-precision numerical computations.