Do you precondition on the left or on the right?

2025/12/04 by Nicole Spillane, Spillane, Nicole, Pierre Matalon +3
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Opinion Dynamics and Social Influence #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2512.05160

openalex created_date 2025/12/04 · openalex publication_date 2025/12/04 · openalex updated_date 2026/07/28

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.

Citations

• Any nonincreasing convergence curves are simultaneously possible for GMRES and weighted GMRES, as well as for left and right preconditioned GMRES
• Improved Polynomial Bounds and Acceleration of GMRES by Solving a min-max Problem on Rectangles, and by Deflating
• New Convergence Analysis of GMRES with Weighted Norms, Preconditioning and Deflation, Leading to a New Deflation Space
• Hermitian Preconditioning for a class of Non-Hermitian Linear Systems

Cited by

• Any nonincreasing convergence curves are simultaneously possible for GMRES and weighted GMRES, as well as for left and right preconditioned GMRES

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