TY - JOUR
T1 - Diagonal Threshold Techniques in Robust Multi-level ILU Preconditioners for General Sparse Linear Systems
AU - Saad, Yousef
AU - Zhang, Jun
PY - 1999
Y1 - 1999
N2 - This paper introduces techniques based on diagonal threshold tolerance when developing multi-elimination and multi-level incomplete LU (ILUM) factorization preconditioners for solving general sparse linear systems. Existing heuristics solely based on the adjacency graph of the matrices have been used to find independent sets and are not robust for matrices arising from certain applications in which the matrices may have small or zero diagonals. New heuristic strategies based on the adjacency graph and the diagonal values of the matrices for finding independent sets are introduced. Analytical bounds for the factorization and preconditioned errors are obtained for the case of a two-level analysis. These bounds provide useful information in designing robust ILUM preconditioners. Extensive numerical experiments are conducted in order to compare robustness and efficiency of various heuristic strategies.
AB - This paper introduces techniques based on diagonal threshold tolerance when developing multi-elimination and multi-level incomplete LU (ILUM) factorization preconditioners for solving general sparse linear systems. Existing heuristics solely based on the adjacency graph of the matrices have been used to find independent sets and are not robust for matrices arising from certain applications in which the matrices may have small or zero diagonals. New heuristic strategies based on the adjacency graph and the diagonal values of the matrices for finding independent sets are introduced. Analytical bounds for the factorization and preconditioned errors are obtained for the case of a two-level analysis. These bounds provide useful information in designing robust ILUM preconditioners. Extensive numerical experiments are conducted in order to compare robustness and efficiency of various heuristic strategies.
KW - Incomplete LU factorization
KW - Krylov subspace methods
KW - Multi-elimination ILU factorization
KW - Multi-level preconditioner
KW - Reordering techniques
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U2 - 10.1002/(sici)1099-1506(199906)6:4<257::aid-nla157>3.0.co;2-%23
DO - 10.1002/(sici)1099-1506(199906)6:4<257::aid-nla157>3.0.co;2-%23
M3 - Article
AN - SCOPUS:0033439932
SN - 1070-5325
VL - 6
SP - 257
EP - 280
JO - Numerical Linear Algebra with Applications
JF - Numerical Linear Algebra with Applications
IS - 4
ER -