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MichaelMaggs (talk | contribs) Adding local short description: "Concept in numerical linear algebra", overriding Wikidata description "sparse approximation of the LU factorization often used as a preconditioner" |
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{{Short description|Concept in numerical linear algebra}}
In [[numerical linear algebra]], an '''incomplete LU factorization''' (abbreviated as '''ILU''') of a [[matrix (mathematics)|matrix]] is a [[sparse matrix|sparse]] approximation of the [[LU factorization]] often used as a [[preconditioner]].
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G(A) := \left\lbrace (i,j) \in \N^2 : A_{ij} \neq 0 \right\rbrace \,,
</math>
which is used to define the conditions a ''sparsity
:<math>
S \subset \left\lbrace 1, \dots , n \right\rbrace^2
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