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Improving the Performance of Sparse LU Matrix Factorization Using a Supernodal Algorithm
Keywords
sparse matrices, linear algebra, LU factorisation
Abstract
In this paper we investigate a method to improve the performance of sparse LU matrix factorization used to solve unsymmetric linear systems, which appear in many mathematical models. We introduced and used the concept of the supernode for unsymmetric matrices in order to use dense matrix operations to perform the LU factorization for sparse matrices. We describe an algorithm that uses supernodes for unsymmetric matrices and we indicate methods to locate these supernodes. Using these ideas we developed a code for sparse LU matrix factorisation. We conducted experiments to evaluate the performance of this algorithm using several sparse matrices. We also made comparisons with other available software packages for sparse LU factorisation.