ILUs and Factorized Approximate Inverses are Strongly Related. Part I: Overview of Results

This paper discusses the relations between a broad class of incomplete LU factorization techniques and factorized sparse approximate inverse techniques based on computing triangular matrices Z;W such that ZAW is approximately diagonal. We will show that most of these approaches are essentially equivalent to approximately inverting the triangular factors obtained from a modi ed incomplete LU factorization of the initial system.

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