Do you precondition on the left or on the right?

TL;DR

This paper reports on a social experiment investigating preferences for left or right preconditioning, providing context, literature review, and analysis of convergence bounds, highlighting potential misconceptions.

Contribution

It offers empirical data on preconditioning preferences, reviews existing literature, and critically analyzes convergence bounds in the context of preconditioning.

Findings

Participants showed varied preferences for left or right preconditioning.

Convergence bounds can sometimes be misleading in assessing preconditioning effectiveness.

The paper provides a comprehensive literature review on preconditioning techniques.

Abstract

This work is a follow-up to a poster that was presented at the DD29 conference. Participants were asked the question: ``Do you precondition on the left or on the right?''. Here we report on the results of this social experiment. We also provide context on left, right and split preconditioning, share our literature review on the topic, and analyze some of the finer points. Two examples illustrate that convergence bounds can sometimes lead to misleading conclusions.