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Towards a recursive iterative preconditioner

Published: 04 April 2013 Publication History

Abstract

Consider a solution of systems of linear equations Ax = b when A is a symmetric positive definite matrix. We solve the equations using a direct method using Cholesky factorization, A = LLT or a preconditioned iterative method. In this paper, we are proposing a new preconditioner based on the iterative recursion to improve the performance of conjugate gradient method. We demonstrate through experiments that our recursive iterative preconditioner improves convergence when it is used as a preconditioner for the conjugate gradient method. We conjecture that the improvements in the quality of preconditioning arise from the ability of our method to generate better approximations to the complete factor.

References

[1]
MatrixMarket, http://math.nist.gov/MatrixMarket
[2]
On preconditionning Schur complement and Schur complement preconditioning, Jun Zhang, ETNA, Vol 10, 2000, pp115--130.
[3]
Preconditining the Schur complement in a hybrid direct/iterative solver, Jeremie Gaidamour and Pascal Henon, SparseDays, 2010.
[4]
Direct Methods for Sparse Linear Systems, Timothy A. Davis, SIAM, 2006.
[5]
Iterative Methods for Sparse Linear Systems, Y. Saad, SIAM, 2003.
[6]
On Block Diagonal And Schur Complement Preconditioning, Jan Mandel, Numerical Mathematik, 58, 79--93, 1990.
[7]
Preconditioning Techniques for Large Linear Systems: A Survey, Michele Benzi, Journal of Computational Physics 182, 418--477, 2002.

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  1. Towards a recursive iterative preconditioner

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    cover image ACM Conferences
    ACMSE '13: Proceedings of the 51st annual ACM Southeast Conference
    April 2013
    224 pages
    ISBN:9781450319010
    DOI:10.1145/2498328
    • General Chair:
    • Ashraf Saad
    Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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    New York, NY, United States

    Publication History

    Published: 04 April 2013

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    Author Tags

    1. iterative method
    2. preconditioner
    3. recursive

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    • Research-article

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    ACM SE'13
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    ACM SE'13: ACM Southeast Regional 2013
    April 4 - 6, 2013
    Georgia, Savannah

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    Overall Acceptance Rate 502 of 1,023 submissions, 49%

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