# Preconditioning via Diagonal Scaling

arXiv: https://arxiv.org/abs/1610.03871 · HTML: https://mlsanity.com/paper/1610.03871/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2016.

## Built on by (most cited first, 1 of 1)

- [Optimal Diagonal Preconditioning](https://mlsanity.com/paper/2209.00809/) (2022)

## Abstract (arXiv)

Interior point methods solve small to medium sized problems to high accuracy in a reasonable amount of time. However, for larger problems as well as stochastic problems, one needs to use first-order methods such as stochastic gradient descent (SGD), the alternating direction method of multipliers (ADMM), and conjugate gradient (CG) in order to attain a modest accuracy in a reasonable number of iterations. In this report, we first discuss heuristics for diagonal scaling. Next, we motivate preconditioning by an example, and then we study preconditioning for a specific splitting form in ADMM called graph projection splitting. Finally we examine the performance of our methods by some numerical examples.