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 …

The linear equations that arise in interior methods for constrained optimization are sparse
symmetric indefinite, and they become extremely ill-conditioned as the interior method …

The subject of sparse matrices has its root in such diverse fields as management science,
power systems analysis, surveying, circuit theory, and structural analysis. Efficient use of …

Large sparse linear systems of equations are ubiquitous in science, engineering and
beyond. This open access monograph focuses on factorization algorithms for solving such …

Combinatorial techniques have become essential tools across the landscape of
computational science, and some of the combinatorial ideas undergirding these tools are …

The solution of trust-region and regularisation subproblems that arise in unconstrained
optimization is considered. Building on the pioneering work of Gay, Moré and Sorensen …

The rapid emergence of multicore machines has led to the need to design new algorithms
that are efficient on these architectures. Here, we consider the solution of sparse symmetric …

Decomposition techniques for linear programming are difficult to extend to conic
optimization problems with general nonpolyhedral convex cones because the conic …

The advent of efficient interior point optimization methods has enabled the tractable solution
of large-scale linear and nonlinear programming (NLP) problems. A prominent example of …

In recent years, a variety of preconditioners have been proposed for use in solving large
sparse linear least-squares problems. These include simple diagonal preconditioning …