Results 31 to 40 of about 649,766 (178)

Kantorovich-type semilocal convergence analysis for inexact Newton methods [PDF]

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   +4 more sources

Semilocal convergence conditions for the secant method, using recurrent functions [PDF]

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.
Ioannis K. Argyros, Saïd Hilout
doaj   +3 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,
Ioannis K. Argyros, Sanjay K. Khattri
doaj   +3 more sources

An exciting Approach to Theoretical Spectroscopy. [PDF]

Adv Sci (Weinh)
ABSTRACT Theoretical spectroscopy, and more generally, electronic‐structure theory, are powerful concepts for describing the complex many‐body interactions in materials. They cover methods from ground‐state properties to lattice excitations and light‐matter interaction, including time‐resolved variants.
Raya-Moreno M, Buccheri A, Dasch NA, Farahani N, Gonzalez Oliva I, Gulans A, Hong S, Hossain M, Kleine H, Kuban M, Lubeck S, Maurer B, Pavone P, Peschel F, Popova-Gorelova D, Qiao L, Richter E, Rigamonti S, Pela RR, Schebek M, Sinha K, Speckhard DT, Stutz J, Tillack S, Tumakov D, Užulis J, Voiculescu M, Vona C, Yang M, Draxl C.   +29 more
europepmc   +2 more sources

On the semilocal convergence of derivative free methods for solving nonlinear equations [PDF]

Journal of Numerical Analysis and Approximation Theory, 2012
We introduce a Derivative Free Method (DFM) for solving nonlinear equations in a Banach space setting. We provide a semilocal convergence analysis for DFM using recurrence relations. Numerical examples validating our theoretical results are also provided
Ioannis K. Argyros, Hongmin Ren
doaj   +3 more sources

On the Convergence of a New Family of Multi-Point Ehrlich-Type Iterative Methods for Polynomial Zeros

Mathematics, 2021
In this paper, we construct and study a new family of multi-point Ehrlich-type iterative methods for approximating all the zeros of a uni-variate polynomial simultaneously.
Petko D. Proinov, Milena D. Petkova
doaj   +1 more source

A New Family of High-Order Ehrlich-Type Iterative Methods

Mathematics, 2021
One of the famous third-order iterative methods for finding simultaneously all the zeros of a polynomial was introduced by Ehrlich in 1967. In this paper, we construct a new family of high-order iterative methods as a combination of Ehrlich’s iteration ...
Petko D. Proinov, Maria T. Vasileva
doaj   +1 more source

A NOTE ON THE SEMILOCAL CONVERGENCE OF CHEBYSHEV’S METHOD [PDF]

Bulletin of the Australian Mathematical Society, 2012
AbstractIn this paper we develop a Kantorovich-like theory for Chebyshev’s method, a well-known iterative method for solving nonlinear equations in Banach spaces. We improve the results obtained previously by considering Chebyshev’s method as an element of a family of iterative processes.
Diloné, Manuel A., García-Olivo, Martín, Gutiérrez, José M.   +2 more
openaire   +2 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

Improving Convergence Analysis of the Newton–Kurchatov Method under Weak Conditions

Computation, 2020
The technique of using the restricted convergence region is applied to study a semilocal convergence of the Newton−Kurchatov method. The analysis is provided under weak conditions for the derivatives and the first order divided differences ...
Ioannis K. Argyros, Stepan Shakhno, Halyna Yarmola   +2 more
doaj   +1 more source