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 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 …

In this work, a systematic review of heuristics for profile reduction of symmetric matrices is
presented. 74 heuristics tested for reduction profile were found. Researchers compared …

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

Many sparse matrix computations can be speeded up if the matrix is first reordered.
Reordering was originally developed for direct methods but it has recently become popular …

A multilevel algorithm for reordering sparse symmetric matrices to reduce the wavefront and
profile is described. The algorithm is a combinatorial algorithm that uses a maximal …

Hundreds of heuristics have been proposed to resolve the problems of bandwidth and
profile reductions since the 1960s. We found 132 heuristics that have been applied to these …

This article focuses on the design and development of a new robust and efficient general-
purpose incomplete Cholesky factorization package HSL_MI28, which is available within the …