The effects of scalings on the performance of a sparse symmetric indefinite solver

Abstract

Scaling is an important part of solving large sparse symmetric linear systems. In a direct method where the analysis is based only on structure it can help by reducing the number of delayed pivots and hence the memory required, the size of the computed factors, and total solution time. In this paper, we examine the effects of scaling on the performance of a sparse symmetric indefinite solver that implements a multifrontal algorithm. We compare several scalings from the mathematical software library HSL, using a large test set of 367 problems from a wide range of practical applications.