Max-plus approximation of the LU decomposition of a matrix

James Hook (University of Manchester)

Frank Adams Room 1, Alan Turing Building,

Max-plus algebra has previously been used in NLA to approximate the size of the eigenvalues (and singular values) of matrices and matrix polynomials. In this talk I will describe a new max-plus method for approximating the size of the entries in the LU factors of a matrix A.
 
This approximation can be used to predict the positions of the larger entries in the LU factors of A and this information can be useful in constructing an ILU preconditioner for A.
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