Incomplete LU factorization: Difference between revisions

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== Stability ==

Concerning the stability of the ILU the following theorem was proven by Meijerink and van der Vorst.<ref>{{Cite journal|last=Meijerink|first=J. A.|last2=Vorst|first2=Van Der|last3=A|first3=H.|date=1977|title=An iterative solution method for linear systems of which the coefficient matrix is a symmetric 𝑀-matrix|url=httphttps://www.ams.org/home/page/|journal=Mathematics of Computation|language=en-US|volume=31|issue=137|pages=148–162|doi=10.1090/S0025-5718-1977-0438681-4|issn=0025-5718|doi-access=free}}</ref>

Let <math> A </math> be an [[M-matrix]], the (complete) LU decomposition given by <math> A=\hat{L} \hat{U} </math>, and the ILU by <math> A=LU-R </math>.