Influence of matrix reordering on the performance of iterative methods for solving linear systems arising from interior point methods for linear programming

Daniele Silva (), Marta Velazco () and Aurelio Oliveira ()
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Daniele Silva: Federal Technological University of Paraná
Marta Velazco: Faculty of Campo Limpo Paulista
Aurelio Oliveira: State University of Campinas

Mathematical Methods of Operations Research, 2017, vol. 85, issue 1, No 7, 97-112

Abstract: Abstract This study analyzes the influence of sparse matrix reordering on the solution of linear systems arising from interior point methods for linear programming. In particular, such linear systems are solved by the conjugate gradient method with a two-phase hybrid preconditioner that uses the controlled Cholesky factorization during the initial iterations and later adopts the splitting preconditioner. This approach yields satisfactory computational results for the solution of linear systems with symmetric positive-definite matrices. Three reordering heuristics are analyzed in this study: the reverse Cuthill–McKee heuristic, the Sloan algorithm, and the minimum degree heuristic. Through numerical experiments, it was observed that these heuristics can be advantageous in terms of accelerating the convergence of the conjugate gradient method and reducing the processing time.

Keywords: Interior point methods; Linear systems; Iterative methods; Preconditioner; Reordering heuristics (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s00186-017-0571-7

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