Hook, James
(2015)
*Max-plus LU.*
[MIMS Preprint]

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## Abstract

We present a new method for the a priori approximation of the order of magnitude of the entries in the LU factors of a matrix A Ã�Â¢Ã�Â�Ã�Â� CnÃ�Â�Ã¢Â�Â�n. We are also able to predict which permutation matrices will be chosen by partial pivoting or complete pivoting Gaussian elimination. Our method uses max- plus algebra and is based purely on the moduli of the entries in the matrix. This approximation can be used in the construction of ILU preconditioners, where the max-plus LU approximation can be used to quickly determine the positions of the largest entries in the LU factors. These positions can subsequently be used as the sparsity pattern for an ILU preconditioner.

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