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http://dx.doi.org/10.14317/jami.2014.389

PERFORMANCE COMPARISON OF PRECONDITIONED ITERATIVE METHODS WITH DIRECT PRECONDITIONERS  

Yun, Jae Heon (Department of Mathematics, Chungbuk National University)
Lim, Hyo Jin (Department of Mathematics, Chungbuk National University)
Kim, Kyoum Sun (Department of Mathematics, Chungbuk National University)
Publication Information
Journal of applied mathematics & informatics / v.32, no.3_4, 2014 , pp. 389-403 More about this Journal
Abstract
In this paper, we first provide comparison results of preconditioned AOR methods with direct preconditioners $I+{\beta}L$, $I+{\beta}U$ and $I+{\beta}(L+U)$ for solving a linear system whose coefficient matrix is a large sparse irreducible L-matrix, where ${\beta}$ > 0. Next we propose how to find a near optimal parameter ${\beta}$ 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.
Keywords
preconditioned AOR method; L-matrix; irreducible matrix; triangular preconditioner; Krylov subspace method;
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