On the Convergence of Conjugate Gradient Variants in Finite Precision Arithmetic

Tyler Chen

A pdf version of this page can be found here.

This page is under construction.

This is a companion piece to the publication:

@article{greenbaum_liu_chen_19

    Author = {Anne Greenbaum, Hexuan Liu, and Tyler Chen}

    Title = {On the Convergence of Conjugate Gradient Variants 

             in Finite Precision Arithmetic.}

    Howpublished = {In progress.}

    Year = {2019}

}

A preprint will be on ArXiV in the near future.

Why should I care?

Need new algorithms to deal with modern HPC architecture. But can’t sacrifice accuracy.

Take advantage of lower precision for ML type applications.

Introduction

If you are not familiar with the Conjugate Gradient method, it may be worth reading this page first.

The Conjugate Gradient algorithm is a widely used method for solving \(Ax=b\) when \(A\) is positive definite (all eigenvalues are positive).

Conjugate Gradient In Finite Precision

Numerical Problems

Avoiding Communication

Concusion