Results 1 to 10 of about 3,416 (193)

Semilocal Convergence of the Extension of Chun’s Method [PDF]

Axioms, 2021
In this work, we use the technique of recurrence relations to prove the semilocal convergence in Banach spaces of the multidimensional extension of Chun’s iterative method. This is an iterative method of fourth order, that can be transferred to the multivariable case by using the divided difference operator.
Alicia Cordero, Javier G. Maimó, Eulalia Martínez, Juan R. Torregrosa, María P. Vassileva   +4 more
openaire   +5 more sources

Extended Semilocal Convergence for the Newton- Kurchatov Method

Matematychni Studii, 2020
We provide a semilocal analysis of the Newton-Kurchatov method for solving nonlinear equations involving a splitting of an operator. Iterative methods have a limited restricted region in general. A convergence of this method is presented under classical Lipschitz conditions.The novelty of our paper lies in the fact that we obtain weaker sufficient ...
H.P. Yarmola, I. K. Argyros, S.M. Shakhno   +2 more
openaire   +4 more sources

Ab Initio Calculation of Energy Gap and Optical Gap of Organic Semiconductors PTCDA and PDI. [PDF]

Chemphyschem
We benchmark electronic structure methods for predicting energy and optical gaps of three organic semiconductors from molecules to crystals. GW is most reliable for crystalline energy levels, while single‐molecule time‐dependent density functional theory with a polarizable continuum model delivers remarkable accuracy for some quantities at a much lower
Hsieh CM, Link T, Maas M, Koschek K, Neudecker T.   +4 more
europepmc   +2 more sources

Semilocal convergence theorem for the inverse-free Jarratt method under new Hölder conditions. [PDF]

ScientificWorldJournal, 2015
Under the new Hölder conditions, we consider the convergence analysis of the inverse-free Jarratt method in Banach space which is used to solve the nonlinear operator equation. We establish a new semilocal convergence theorem for the inverse-free Jarratt
Zhao Y, Lin R, Šmarda Z, Khan Y, Chen J, Wu Q.   +5 more
europepmc   +2 more sources

Semilocal Convergence Analysis for Inexact Newton Method under Weak Condition [PDF]

Abstract and Applied Analysis, 2012
Under the hypothesis that the first derivative satisfies some kind of weak Lipschitz conditions, a new semilocal convergence theorem for inexact Newton method is presented. Unified convergence criteria ensuring the convergence of inexact Newton method are also established. Applications to some special cases such as the Kantorovich type conditions and γ‐
Xu, Xiubin, Xiao, Yuan, Liu, Tao
openaire   +4 more sources

Extensions to Extended Tight-Binding Methods for Transition-Metal Containing Systems. [PDF]

J Comput Chem
We present a new GFN2‐xTB implementation with a geometric direct minimization scheme and a Hubbard‐U correction. We demonstrate that the Hubbard correction improves linearity of the elctronic energy, stabilizes SCF convergence, and enables more accurate spin‐gap predictions in narrow application domains such as specific iron‐containing complexes ...
Moradi S, Tomann R, Head-Gordon M, Stein CJ.   +3 more
europepmc   +2 more sources

Convergence analysis of iterative compositions in nonlinear modeling: exploring semilocal and local convergence phenomena

Journal of Numerical Analysis and Approximation Theory
In this work, a comprehensive analysis of a multi-step iterative composition for nonlinear equation is performed, providing insights into both local and semilocal convergence properties. The analysis covers a wide range of applications, elucidating the parameters affecting both local and semilocal convergence and offering insightful information for ...
Sunil Kumar, null Janak Raj Sharma, null Ioannis K. Argyros   +2 more
openaire   +3 more sources

A highly accurate family of stable and convergent numerical solvers based on Daftardar-Gejji and Jafari decomposition technique for systems of nonlinear equations. [PDF]

MethodsX
This study introduces a family of root-solvers for systems of nonlinear equations, leveraging the Daftardar–Gejji and Jafari Decomposition Technique coupled with the midpoint quadrature rule.
Qureshi S, Argyros IK, Jafari H, Soomro A, Gdawiec K.   +4 more
europepmc   +2 more sources

Semilocal convergence conditions for the secant method, using recurrent functions

Journal of Numerical Analysis and Approximation Theory, 2011
Using our new concept of recurrent functions, we present new sufficient convergence conditions for the secant method to a locally unique solution of a nonlinear equation in a Banach space. We combine Lipschitz and center-Lipschitz conditions on the divided difference operator to obtain the semilocal convergence ...
Ioannis K. Argyros, Saïd Hilout
doaj   +5 more sources

An improved semilocal convergence analysis for the midpoint method

Journal of Numerical Analysis and Approximation Theory, 2016
We expand the applicability of the midpoint method for approximating a locally unique solution of nonlinear equations in a Banach space setting. Our majorizing sequences are finer than the known results in scientific literature [1,3,4,5,6,7,8,9,10,11,19,20,21,23] and the convergence criteria can be weaker.
Ioannis K. Argyros, Sanjay K. Khattri
openaire   +4 more sources