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On Convergence of an Accelerated Modified Newton Method for Nonlinear Equations — arXiv:2608.22060

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.22060
License (as archived): CC0-1.0
Archived: 2026-10-18T08:27:29.948Z
SHA-256 of the archived text: d6b2159dcb1395db8fa52639620eec988bba073025e45d22eefcd2cce4fb450b
Stable URL of this page: https://metraipolis.com/documento/dc_8ea0fb303995

How to cite

On Convergence of an Accelerated Modified Newton Method for Nonlinear Equations — arXiv:2608.22060 — arXiv (en), https://arxiv.org/abs/2608.22060 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_8ea0fb303995 (Metraipolis archive dc_8ea0fb303995, sha256 d6b2159dcb1395db8fa52639620eec988bba073025e45d22eefcd2cce4fb450b)

BibTeX

@misc{dc8ea0fb303995,
  title = {On Convergence of an Accelerated Modified Newton Method for Nonlinear Equations — arXiv:2608.22060},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.22060},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_8ea0fb303995; sha256 d6b2159dcb1395db8fa52639620eec988bba073025e45d22eefcd2cce4fb450b},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.22060. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Newton's iteration is a fundamental tool for root-finding and numerical solutions of systems of equations. The iteration rapidly refines the initial approximation to the exact root, and in general the convergence is quadratic. Since the method requires finding the function value and its derivative at each iteration, in some cases, it may not converge. This is because the value of the derivative gets close to zero. In this paper, we introduce a modified and stable algorithm of Newton's iteration method that addresses this issue, reduces computational cost, and improves efficiency. In addition. we analyze the convergence properties of the modified method to demonstrate its effectiveness.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-25 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2608.22060 — 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 2026-10-18T08:27:23.835Z dalla pagina https://arxiv.org/catchup/math.NA/2026-08-25?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).