Lecture Notes on Support Preconditioning

TL;DR

This paper provides comprehensive lecture notes on support preconditioning techniques for large sparse linear systems, covering theoretical foundations and practical methods including support theory and Laplacian-based preconditioners.

Contribution

It offers an in-depth overview of support preconditioning methods, integrating support theory with applications to Laplacians and spanning tree preconditioning, originally compiled in 2007.

Findings

Detailed explanation of support preconditioning techniques

Connections between support theory and Laplacian solvers

Introduction to augmented maximum-spanning tree preconditioning

Abstract

These are lectures notes on support preconditioning, originally written in 2007. The notes cover large sparse linear systems of equations, krylov subspace solvers for symmetric diagonally dominant linear systems, sparse Cholesky, support theory, Laplacians, and augmented maximum-spanning tree preconditioning.