Ball convergence for combined three-step methods under generalized conditions in Banach space [PDF]
, 2020 We give a local convergence analysis for an eighth-order convergent method in order to approximate a locally unique solution of nonlinear equation for Banach space valued operators. In contrast to the earlier studies using hypotheses up to the seventh Fr´
ARGYROS , Ioannis K. +3 more
core +2 more sources
Approximating Multiple Roots of Applied Mathematical Problems Using Iterative Techniques [PDF]
, 2023 [EN] In this study, we suggest a new iterative family of iterative methods for approximating the roots with multiplicity in nonlinear equations. We found a lack in the approximation of multiple roots in the case that the nonlinear operator be non ...
Arora, Himani +3 more
core +1 more source
THE HYPERBOLIC QUADRATIC EIGENVALUE PROBLEM
Forum of Mathematics, Sigma, 2015 The hyperbolic quadratic eigenvalue problem (HQEP) was shown to admit Courant–Fischer type min–max principles in 1955 by Duffin and Cauchy type interlacing inequalities in 2010 by Veselić.
XIN LIANG, REN-CANG LI
doaj +1 more source
Iterative Convergence with Banach Space Valued Functions in Abstract Fractional Calculus
Annals of the West University of Timisoara: Mathematics and Computer Science, 2017 The goal of this paper is to present a semi-local convergence analysis for some iterative methods under generalized conditions. The operator is only assumed to be continuous and its domain is open. Applications are suggested including Banach space valued
Anastassiou George A. +1 more
doaj +1 more source
Some issues related to double roundings [PDF]
, 2013 International audienceDouble rounding is a phenomenon that may occur when different floating- point precisions are available on the same system. Although double rounding is, in general, innocuous, it may change the behavior of some useful small floating ...
Martin-Dorel, Érik +2 more
core +3 more sources
Local convergence for an eighth order method for solving equations and systems of equations
Nonlinear Engineering, 2019 The aim of this study is to extend the applicability of an eighth convergence order method from the k−dimensional Euclidean space to a Banach space setting.
Argyros Ioannis K., George Santhosh
doaj +1 more source
The ROMES method for statistical modeling of reduced-order-model error [PDF]
, 2014 This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive `error indicators' to a ...
Carlberg, Kevin, Drohmann, Martin
core +2 more sources
Derivative-Free King's Scheme for Multiple Zeros of Nonlinear Functions [PDF]
, 2021 [EN] There is no doubt that the fourth-order King's family is one of the important ones among its counterparts. However, it has two major problems: the first one is the calculation of the first-order derivative; secondly, it has a linear order of ...
Ahlfors +7 more
core +1 more source
Ball Comparison between Three Sixth Order Methods for Banach Space Valued Operators [PDF]
, 2020 Three methods of sixth order convergence are tackled for approximating the solution of an equation defined on the finitely dimensional Euclidean space. This convergence requires the existence of derivatives of, at least, order seven.
Argyros, Ioannis K. +2 more
core +1 more source
Error structures and parameter estimation [PDF]
, 2004 This article proposes and studies a link between statistics and the theory of Dirichlet forms used to compute errors. The error calculus based on Dirichlet forms is an extension of classical Gauss' approach to error propagation.
Bouleau, Nicolas, Chorro, Christophe
core +4 more sources