• Title/Summary/Keyword: scaled preconditioner

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FAST ONE-PARAMETER RELAXATION METHOD WITH A SCALED PRECONDITIONER FOR SADDLE POINT PROBLEMS

  • OH, SEYOUNG;YUN, JAE HEON
    • Journal of applied mathematics & informatics
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    • v.34 no.1_2
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    • pp.85-94
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    • 2016
  • In this paper, we first propose a fast one-parameter relaxation (FOPR) method with a scaled preconditioner for solving the saddle point problems, and then we present a formula for finding its optimal parameter. To evaluate the effectiveness of the proposed FOPR method with a scaled preconditioner, numerical experiments are provided by comparing its performance with the existing one or two parameter relaxation methods with optimal parameters such as the SOR-like, the GSOR and the GSSOR methods.

ACCELERATION OF ONE-PARAMETER RELAXATION METHODS FOR SINGULAR SADDLE POINT PROBLEMS

  • Yun, Jae Heon
    • Journal of the Korean Mathematical Society
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    • v.53 no.3
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    • pp.691-707
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    • 2016
  • In this paper, we first introduce two one-parameter relaxation (OPR) iterative methods for solving singular saddle point problems whose semi-convergence rate can be accelerated by using scaled preconditioners. Next we present formulas for finding their optimal parameters which yield the best semi-convergence rate. Lastly, numerical experiments are provided to examine the efficiency of the OPR methods with scaled preconditioners by comparing their performance with the parameterized Uzawa method with optimal parameters.