This article surveys preconditioning techniques for the iterative solution of large linear
systems, with a focus on algebraic methods suitable for general sparse matrices. Covered …

The computational solution of problems can be restricted by the availability of solution
methods for linear (ized) systems of equations. In conjunction with iterative methods …

In the six years that have passed since the publication of the first edition of this book,
iterative methods for linear systems have made good progress in scientific and engineering …

Excerpt More than 25 years have passed since the first edition of this book was published in
1996. Least squares and least-norm problems have become more significant with every …

This article presents new results on using a greedy algorithm, orthogonal matching pursuit
(OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a …

Based on extensive research by Henk van der Vorst, this book presents an overview of a
number of Krylov projection methods for the solution of linear systems of equations. Van der …

Linear-scaling methods, or methods, have computational and memory requirements which
scale linearly with the number of atoms in the system, N, in contrast to standard approaches …

This paper studies a difficult and fundamental problem that arises throughout electrical
engineering, applied mathematics, and statistics. Suppose that one forms a short linear …

This dissertation focuses on efficiently forming reduced-order models for large, linear
dynamic systems. Projections onto unions of Krylov subspaces lead to a class of reduced …

We describe a quantum algorithm that generalizes the quantum linear system algorithm
[Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] to arbitrary problem specifications. We …