TY - JOUR

T1 - ILUT

T2 - A dual threshold incomplete LU factorization

AU - Saad, Yousef

PY - 1994

Y1 - 1994

N2 - In this paper we describe an Incomplete LU factorization technique based on a strategy which combines two heuristics. This ILUT factorization extends the usual ILU(O) factorization without using the concept of level of fill‐in. There are two traditional ways of developing incomplete factorization preconditioners. The first uses a symbolic factorization approach in which a level of fill is attributed to each fill‐in element using only the graph of the matrix. Then each fill‐in that is introduced is dropped whenever its level of fill exceeds a certain threshold. The second class of methods consists of techniques derived from modifications of a given direct solver by including a dropoff rule, based on the numerical size of the fill‐ins introduced, traditionally referred to as threshold preconditioners. The first type of approach may not be reliable for indefinite problems, since it does not consider numerical values. The second is often far more expensive than the standard ILU(O). The strategy we propose is a compromise between these two extremes.

AB - In this paper we describe an Incomplete LU factorization technique based on a strategy which combines two heuristics. This ILUT factorization extends the usual ILU(O) factorization without using the concept of level of fill‐in. There are two traditional ways of developing incomplete factorization preconditioners. The first uses a symbolic factorization approach in which a level of fill is attributed to each fill‐in element using only the graph of the matrix. Then each fill‐in that is introduced is dropped whenever its level of fill exceeds a certain threshold. The second class of methods consists of techniques derived from modifications of a given direct solver by including a dropoff rule, based on the numerical size of the fill‐ins introduced, traditionally referred to as threshold preconditioners. The first type of approach may not be reliable for indefinite problems, since it does not consider numerical values. The second is often far more expensive than the standard ILU(O). The strategy we propose is a compromise between these two extremes.

KW - Incomplete LU

KW - Preconditioning

KW - Threshold strategies

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U2 - 10.1002/nla.1680010405

DO - 10.1002/nla.1680010405

M3 - Article

AN - SCOPUS:84985408358

SN - 1070-5325

VL - 1

SP - 387

EP - 402

JO - Numerical Linear Algebra with Applications

JF - Numerical Linear Algebra with Applications

IS - 4

ER -