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 …

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

Algebraic multigrid (AMG) solves linear systems based on multigrid principles, but in a way
that only depends on the coefficients in the underlying matrix. The author begins with a basic …

This paper investigates the properties of smoothers in the context of algebraic multigrid
(AMG) running on parallel computers with potentially millions of processors. The …

Algebraic multigrid methods continue to grow in robustness as effective solvers for the large
and sparse linear systems of equations that arise in many applications. Unlike geometric …

We develop an algebraic multigrid (AMG) setup scheme based on the bootstrap framework
for multiscale scientific computation. Our approach uses a weighted least squares definition …

The aim of this work is to compare algebraic multigrid (AMG) preconditioned GMRES
methods for solving the nonsymmetric and positive definite linear systems of algebraic …

Algebraic multigrid (AMG) solvers and preconditioners are some of the fastest numerical
methods to solve linear systems, particularly in a parallel environment, scaling to hundreds …

This article has two main objectives: one is to describe some extensions of an adaptive
Algebraic Multigrid (AMG) method of the form previously proposed by the first and third …

This paper provides a unified and detailed presentation of root-node--style algebraic
multigrid (AMG). AMG is a popular and effective iterative method for solving large, sparse …