Wilkinson defined a sparse matrix as one with enough zeros that it pays to take advantage of
them. 1 This informal yet practical definition captures the essence of the goal of direct …

This book presents the fundamentals of sparse matrix algorithms, from theory to algorithms
and data structures to working code. The focus is on direct methods for solving systems of …

The Handbook of Linear Algebra provides comprehensive coverage of linear algebra
concepts, applications, and computational software packages in an easy-to-use handbook …

A new method for sparse LU factorization is presented that combines a column pre-ordering
strategy with a right-looking unsymmetric-pattern multifrontal numerical factorization. The …

Sparse Gaussian elimination with partial pivoting computes the factorization PAQ= LU of a
sparse matrix A, where the row ordering P is selected during factorization using standard …

We investigate the use of low-rank approximations to reduce the cost of sparsedirect
multifrontal solvers. Among the different matrix representations that havebeen proposed to …

We consider ways of implementing preordering and scaling for symmetric systems and show
the effect of using this technique with a multifrontal code for sparse symmetric indefinite …

Most state-of-the-art ordering schemes for sparse matrices are a hybrid of a bottom-up
method such as minimum degree and a top-down scheme such as George's nested …

The minimum degree and minimum local fill algorithms are two bottom-up heuristics for
reordering a sparse matrix prior to factorization. Minimum degree chooses a node of least …

Direct methods for the solution of sparse systems of linear equations are used in a wide
range of numerical simulation applications. Such methods are based on the decomposition …