Since the early 1990s, there has been a strongly increasing demand for more efficient
methods to solve large sparse, unstructured linear systems of equations. For practically …

Various graphs such as web or social networks may contain up to trillions of edges.
Compressing such datasets can accelerate graph processing by reducing the amount of I/O …

Analysis and computation, the most important and indispensable methods for processing
matrices, are closely related but two significantly different areas. The former focuses more on …

This paper provides an overview of AMG methods for solving large-scale systems of
equations, such as those from discretizations of partial differential equations. AMG is often …

Driven by the need to solve linear systems arising from problems posed on extremely large,
unstructured grids, there has been a recent resurgence of interest in algebraic multigrid …

Our goal in this paper is to show that many of the tools of signal processing, adapted Fourier
and wavelet analysis can be naturally lifted to the setting of digital data clouds, graphs, and …

We present a new method for automatic segmentation of heterogeneous image data that
takes a step toward bridging the gap between bottom-up affinity-based segmentation …

A rigorous two-level theory is developed for general symmetric matrices (and nonsymmetric
ones using Kaczmarz relaxation), without assuming any regularity, not even any grid …

This monograph is the first to provide a comprehensive, self-contained and rigorous
presentation of some of the most powerful preconditioning methods for solving finite element …

Laplacian matrices of graphs arise in large-scale computational applications such as
semisupervised machine learning; spectral clustering of images, genetic data, and web …