The Handbook of Linear Algebra provides comprehensive coverage of linear algebra
concepts, applications, and computational software packages in an easy-to-use handbook …

We present a randomized algorithm that on input a symmetric, weakly diagonally dominant n-
by-n matrix A with m nonzero entries and an n-vector b produces an ̃x such that ‖̃x …

We present an algorithm that on input of an n-vertex m-edge weighted graph G and a value
k produces an incremental sparsifier ̂G with n-1+m/k edges, such that the relative condition …

We show how to perform sparse approximate Gaussian elimination for Laplacian matrices.
We present a simple, nearly linear time algorithm that approximates a Laplacian by the …

In this paper we show how to accelerate randomized coordinate descent methods and
achieve faster convergence rates without paying per-iteration costs in asymptotic running …

In this paper, we present a simple combinatorial algorithm that solves symmetric diagonally
dominant (SDD) linear systems in nearly-linear time. It uses little of the machinery that …

We present an improved algorithm for solving symmetrically diagonally dominant linear
systems. On input of an n× n symmetric diagonally dominant matrix A with m non-zero …

We show an algorithm for solving symmetric diagonally dominant (SDD) linear systems with
m non-zero entries to a relative error of ε in O (m log1/2 n log cn log (1/ε)) time. Our approach …

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

Can linear systems be solved faster than matrix multiplication? While there has been
remarkable progress for the special cases of graph structured linear systems, in the general …