On threshold pivoting in the multifrontal method for sparse indefinite systems

Abstract

A simple modification to the numerical pivot selection criteria in the multifrontal scheme of Duff and Reid for sparse symmetric matrix factorization is presented. For a given threshold value, the modification allows a broader choice of block 2 X 2 pivots owing to a less restrictive pivoting condition. It also extends the range of permissible threshold values from [0, 1/2) to [0, 0.6404). Moreover, the bound on element growth for stability consideration in the modified scheme is nearly the same as that of the original strategy. © 1987, ACM. All rights reserved.