On the generalization of the Newton–Kantorovich theorem for nonlinear operator equations

UDC 517.98, 519.61 We construct a modification of the classical Newton-Kantorovich method for nonlinear operator equations whose linearization gives equations that are, as a rule, solvable. For finding the solution of a nonlinear operator equation, we propose to use an iterative scheme with quadrati...

Full description

Saved in:
Bibliographic Details
Date:2026
Main Authors: Chuiko, S., Nesmelova, O., Чуйко, Сергій, Нєсмєлова, Ольга
Format: Article
Language:Ukrainian
Published: Institute of Mathematics, NAS of Ukraine 2026
Online Access:https://umj.imath.kiev.ua/index.php/umj/article/view/9888
Tags: Add Tag
No Tags, Be the first to tag this record!
Journal Title:Ukrains’kyi Matematychnyi Zhurnal
Download file: Pdf

Institution

Ukrains’kyi Matematychnyi Zhurnal
Description
Summary:UDC 517.98, 519.61 We construct a modification of the classical Newton-Kantorovich method for nonlinear operator equations whose linearization gives equations that are, as a rule, solvable. For finding the solution of a nonlinear operator equation, we propose to use an iterative scheme with quadratic convergence. In particular, we establish solvability conditions and construct an iterative procedure aimed at finding the solution of the generalized Riccati equation.
DOI:10.3842/umzh.v78i3-4.9888