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 …

Interior Point Methods for Linear Optimization is a comprehensive, thorough textbook on
interior point methods (IPMs). The era of IPMs was initiated by N. Karmarkar's 1984 paper …

In the nearly seven years since I finished writing the first edition of this book research on the
accuracy and stability of numerical algorithms has continued to flourish and mature. Our …

Large linear systems of saddle point type arise in a wide variety of applications throughout
computational science and engineering. Due to their indefiniteness and often poor spectral …

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 …

Interior methods are an omnipresent, conspicuous feature of the constrained optimization
landscape today, but it was not always so. Primarily in the form of barrier methods, interior …

The first comprehensive review of the theory and practice of one oftoday's most powerful
optimization techniques. The explosive growth of research into and development of …

Sparse matrix factorization algorithms for general problems are typically characterized by
irregular memory access patterns that limit their performance on parallel-vector …

We introduce a new code for the direct solution of sparse symmetric linear equations that
solves indefinite systems with 2× 2 pivoting for stability. This code, called MA57, is in HSL …

In this paper we consider the solution of linear systems of saddle point type by
preconditioned Krylov subspace methods. A preconditioning strategy based on the …