article · ArXiv.org · 2026

Convergence Analysis of the Random Bisection Method

Ludovick Bouthat, Philippe-André Luneau, Philippe Petitclerc

Cited by 0Open access

Abstract

We propose a generalized version of the bisection method where the cutting point between the two subintervals is chosen at random following an arbitrary distribution. We compute expected convergence rates with respect to any arbitrary a priori distribution for the position of the root in the initial interval and proved that it depends only on the the expectation $\mathbb{E}[c(1-c)]$ of the cut $c$. We also provide a generalization of the method for $K$ random cuts and study its convergence properties. Most probabilistic derivations are kept fairly simple for the ease of understanding of a larger audience. Our theoretical results are then validated numerically using statistical simulation.

Cite this paper

APA 7

Bouthat, L., Luneau, P.-A., & Petitclerc, P. (2026). Convergence Analysis of the Random Bisection Method. ArXiv.org.

MLA 9

Bouthat, Ludovick, et al. “Convergence Analysis of the Random Bisection Method.” ArXiv.org, 2026.

Chicago

Bouthat, Ludovick, Philippe-André Luneau, and Philippe Petitclerc. 2026. “Convergence Analysis of the Random Bisection Method.” ArXiv.org.

Harvard

Bouthat, L., Luneau, P.-A. and Petitclerc, P. (2026) ‘Convergence Analysis of the Random Bisection Method’, ArXiv.org.

BibTeX

@article{bouthat2026convergence,
  title = {{Convergence Analysis of the Random Bisection Method}},
  author = {Bouthat, Ludovick and Luneau, Philippe-André and Petitclerc, Philippe},
  journal = {ArXiv.org},
  year = {2026}
}

Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.