A Novel Approach to Find Pseudo–peripheral Vertices for Snay’s Heuristic

Sanderson Gonzaga de Oliveira, Júnior A. B. Bernardes


The solution of linear systems represented by Ax = b is fundamental in many numerical simulations in science and engineering. Reducing the profile of A can reduce the storage requirements and time processing costs of solving such linear systems. In this work, we propose a generalized algorithm for finding pseudo–peripheral vertices for Snay’s heuristic. In experiment performed on 36 instances contained in the Harwell-Boeing and SuiteSparse matrix collections, it has been found that the number of pseudo– peripheral vertices selected in Snay’s heuristic may be suitable for small instances, but it is insufficient to obtain reasonable results in instances that are not small. This paper recommends to select up to 26% (0.3%) of pseudo–peripheral vertices in relation to the instance size when applied to instances smaller than 3,000 (larger than 20,000) vertices.


Profile reduction; sparse matrix; reordering algorithms.

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M. Benzi. Preconditioning techniques for large linear systems: a survey. Journal of Computational Physics, 182:418–477, 2002.

Authors. Title, Journal, 51:221–230, 2015.

I. S. Duff, R. G. Grimes, and J. G. Lewis. Sparse matrix test problems. ACM

Transactions on Mathematical Software, 15(1):1–14, 1989.

G. C. Everstine. A comparison of three resequencing algorithms for the reduction of matrix profile and wavefront. International Journal for Numerical

Methods in Engineering, 14:837–853, 1979.

S. L. Gonzaga de Oliveira e G. O. Chagas. Introdução a heurísticas para redução de largura de banda de matrizes. SBMAC, São Carlos, 2014.

Y. X. Lin and J. J. Yuan. Profile minimization problem for matrices and graphs. Acta Mathematicae Applicatae Sinica, 10(1):107–122, 1994.

J. K. Reid and J. A. Scott. Reducing the Total Bandwidth of a Sparse Un-

symmetric Matrix. SIAM Journal on Matrix Analysis and Applications, 28(3):

–821, 2006.

R. A. Snay. Reducing the profile of sparse symmetric matrices. Bulletin Geodesique, 50(4):341–352, 1976.

DOI: https://doi.org/10.5540/tema.2018.019.01.1

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TEMA - Trends in Applied and Computational Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
ISSN: 1677-1966  (print version),  2179-8451  (online version)

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