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Adversarial Wronskians: A proof of the Kung--Traub conjecture — arXiv:2610.40660

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.40660
License (as archived): CC0-1.0
Archived: 2026-11-02T07:58:28.146Z
SHA-256 of the archived text: 1fc51041e04969058c6b3fb6a6c8da7ee567104e5cbba95db98db7bd5c148a53
Stable URL of this page: https://metraipolis.com/documento/dc_dc3e87f80ccc

How to cite

Adversarial Wronskians: A proof of the Kung--Traub conjecture — arXiv:2610.40660 — arXiv (en), https://arxiv.org/abs/2610.40660 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_dc3e87f80ccc (Metraipolis archive dc_dc3e87f80ccc, sha256 1fc51041e04969058c6b3fb6a6c8da7ee567104e5cbba95db98db7bd5c148a53)

BibTeX

@misc{dcdc3e87f80ccc,
  title = {Adversarial Wronskians: A proof of the Kung--Traub conjecture — arXiv:2610.40660},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.40660},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_dc3e87f80ccc; sha256 1fc51041e04969058c6b3fb6a6c8da7ee567104e5cbba95db98db7bd5c148a53},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.40660. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We prove the Kung--Traub conjecture: a deterministic stationary root-finding method without memory, using at most $n$ real scalar function or derivative evaluations per iteration, cannot have local order greater than $2^{n-1}$ on every real analytic function with a simple zero. For $n\geq2$, the bound is attained by the methods of Kung and Traub. The local estimate is required at every sufficiently close starting point, with constants that may depend on the function. Evaluation points and derivative orders may be chosen adaptively, and the rules for choosing them and processing the data are unrestricted. The proof uses a localisation property of polynomial Wronskians to obtain a lower bound at each fixed scale. A diagonal construction then gives one entire function, with derivative bounded above and below on the real line, for which every larger order fails. We also obtain a sharper bound when evaluations are made in prescribed groups, and prove the corresponding result for complex scalar evaluations. The results of this paper are also formally verified in Lean.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.NA, nuovi lavori del giorno).
Categorie arXiv: Numerical Analysis (math.NA) ; Computational Complexity (cs.CC); Classical Analysis and ODEs (math.CA).
Pagina del lavoro: https://arxiv.org/abs/2610.40660 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-02T07:42:30.654Z dalla pagina https://arxiv.org/list/math.NA/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).