Results 71 to 80 of about 677,232 (187)

Weaker convergence conditions for the secant method [PDF]

, 2008
summary:In the paper by Hilout and Piétrus (2006) a semilocal convergence analysis was given for the secant-like method to solve generalized equations using Hölder-type conditions introduced by the first author (for nonlinear equations).
Saïd Hilout, Ioannis K. Argyros, Hilout, Said, Argyros, Ioannis K.   +3 more
core   +1 more source

Extended convergence of two-step iterative methods for solving equations with applications

Journal of Numerical Analysis and Approximation Theory
The convergence of two-step iterative methods of third and fourth order of convergence are studied under weaker hypotheses than in earlier works using our new idea of the restricted convergence region.
Ioannis K. Argyros, Santhosh George
doaj   +1 more source

Newton's method in Riemannian manifolds

Journal of Numerical Analysis and Approximation Theory, 2008
Using more precise majorizing sequences than before [1], [8], and under the same computational cost, we provide a finer semilocal convergence analysis of Newton's method in Riemannian manifolds with the following advantages: larger convergence domain ...
Ioannis K. Argyros
doaj   +2 more sources

Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the String‐Theoretical Swampland Programme

Fortschritte der Physik, Volume 74, Issue 4, April 2026.
Abstract String theory has strong implications for cosmology, implying the absence of a cosmological constant, ruling out single‐field slow‐roll inflation, and that black holes decay. The origins of these statements are elucidated within the string‐theoretical swampland programme.
Kay Lehnert
wiley   +1 more source

Convergence of Newton's method under Vertgeim conditions: new extensions using restricted convergence domains [PDF]

, 2016
We present new sufficient convergence conditions for the semilocal convergence ofNewton’s method to a locally unique solution of a nonlinear equation in a Banach space.We use H¨older and center H¨older conditions, instead of just H¨older conditions, for ...
M.A. Hernández-Verón [0000-0001-5478-2958], I. K. Argyros, J.A. Ezquerro [0000-0001-8120-167X], A. A. Magreñán [0000-0002-6991-5706]   +3 more
core  

Robust convergence of Newton's method for cone inclusion problem

, 2018
Capítulo del libro "Contemporary study of iterative methods: convergence, dynamics and applications"In this chapter, motivated by the idea of the restricted convergence domains, we present a convergence analysis of Newton's method for cone inclusion ...
Argyros, Ioannis K, Magreñán, Á. Alberto, Á. Alberto Magreñán, Ioannis K. Argyros, Magreñán, Á. Alberto (1)   +4 more
core   +1 more source

Extended convergence results for the Newton–Kantorovich iteration

, 2015
We present new semilocal and local convergence results for the Newton–Kantorovich method. These new results extend the applicability of the Newton–Kantorovich method on approximate zeros by improving the convergence domain and ratio given in earlier ...
Argyros, Ioannis K, Magreñán, Á. Alberto, Argyros, Ioannis K., Magreñán, Á. Alberto (1), Magreñán, Á. Alberto [0000-0002-6991-5706]   +4 more
core   +2 more sources

Semilocal convergence of a Secant-type method under weak Lipschitz conditions in Banach spaces [PDF]

, 2018
[EN] The semilocal convergence of double step Secant method to approximate a locally unique solution of a nonlinear equation is described in Banach space setting. Majorizing sequences are used under the assumption that the first-order divided differences
Abhimanyu Kumar, Eulalia Martínez, D.K. Gupta, Sukhjit Singh, Singh, Sukhjit, Kumar, A., Gupta, D.K., Martínez Molada, Eulalia   +7 more
core   +1 more source

Kantorovich-type semilocal convergence analysis for inexact Newton methods

Journal of Computational and Applied Mathematics, 2011
The article deals with the iteration \[ x_{n+1} = x_n - F'(x_n)^{-1}(F(x_n) + r_n), \quad n = 0,1,2,\dots \] for approximately solving a nonlinear operator equation \(F(x) = 0\) with an operator \(F\) acting between two Banach spaces \(X\) and \(Y\). The authors formulate some natural conditions under that the iteration under consideration converges to
Ioannis K. Argyros, Hongmin Ren
openaire   +3 more sources

Semilocal Convergence Analysis for MMN-HSS Methods under Hölder Conditions

, 2017
Multi-step modified Newton-HSS (MMN-HSS) methods, which are variants of inexact Newton methods, have been shown to be competitive for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices. Previously, we established
Yang Li, Xue-Ping Guo
core   +1 more source