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PERFORMANCE COMPARISON OF PRECONDITIONED ITERATIVE METHODS WITH DIRECT PRECONDITIONERS
PERFORMANCE COMPARISON OF PRECONDITIONED ITERATIVE METHODS WITH DIRECT PRECONDITIONERS
Journal of applied mathematics & informatics. 2014. May, 32(3_4): 389-403
  • Received : November 15, 2013
  • Published : May 30, 2014
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Yun Jae Heon
Lim Hyo Jin
Kim Kyoum Sun

Abstract
In this paper, we first provide comparison results of preconditioned AOR methods with direct preconditioners <TEX>$I+{\beta}L$</TEX>, <TEX>$I+{\beta}U$</TEX> and <TEX>$I+{\beta}(L+U)$</TEX> for solving a linear system whose coefficient matrix is a large sparse irreducible L-matrix, where <TEX>${\beta}$</TEX> > 0. Next we propose how to find a near optimal parameter <TEX>${\beta}$</TEX> for which Krylov subspace method with these direct preconditioners performs nearly best. Lastly numerical experiments are provided to compare the performance of preconditioned iterative methods and to illustrate the theoretical results.
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