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

Author

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  • Daniele Silva

    (Federal Technological University of Paraná)

  • Marta Velazco

    (Faculty of Campo Limpo Paulista)

  • Aurelio Oliveira

    (State University of Campinas)

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.

Suggested Citation

  • Daniele Silva & Marta Velazco & Aurelio Oliveira, 2017. "Influence of matrix reordering on the performance of iterative methods for solving linear systems arising from interior point methods for linear programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(1), pages 97-112, February.
    • Handle: RePEc:spr:mathme:v:85:y:2017:i:1:d:10.1007_s00186-017-0571-7
    DOI: 10.1007/s00186-017-0571-7
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    References listed on IDEAS

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    1. Edward Rothberg & Bruce Hendrickson, 1998. "Sparse Matrix Ordering Methods for Interior Point Linear Programming," INFORMS Journal on Computing, INFORMS, vol. 10(1), pages 107-113, February.
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