Results 21 to 30 of about 13,410 (248)
Improved convergence ball and error analysis of Müller's method
Boletim da Sociedade Paranaense de Matemática, 2022 We present an improved convergence analysis of Müller's method for solving nonlinear equation under conditions that the divided differences of order one of the involved function satisfy the Lipschitz conditions. Our result improves the earlier work in literature. Numerical examples are presented to illustrate the theoretical results.
Ioannis K. Argyros +2 more
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Extended High Order Algorithms for Equations under the Same Set of Conditions
Algorithms, 2021 A variety of strategies are used to construct algorithms for solving equations. However, higher order derivatives are usually assumed to calculate the convergence order.
Ioannis K. Argyros +5 more
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Ball Convergence for Higher Order Methods Under Weak Conditions
Journal of Mathematical Study, 2021 We present a local convergence analysis for higher order methods in order to approximate a locally unique solution of an equation in a Banach space setting. In earlier studies, Taylor expansions and hypotheses on higher order Fréchet-derivatives are used. We expand the applicability of these methods using only hypotheses on the first Fréchet derivative.
Ioannis K. Argyros, Santhosh George
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Ball Convergence for eighth order method
, 2017 Consider the problem of approximating a locally unique solution x of the nonlinear equation F(x) = 0, (21.1) where F is a Fréchet-differentiable operator defined on a convex subset D of a Banach space X with values in a Banach space Y. The equation (21.1) covers wide range of problems in classical analysis and applications [1-30]. Closed form solutions
Argyros, Ioannis K +1 more
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Heavy Ball Restarted CMRH Methods for Linear Systems
Mathematical and Computational Applications, 2018 The restarted CMRH method (changing minimal residual method based on the Hessenberg process) using fewer operations and storage is an alternative method to the restarted generalized minimal residual method (GMRES) method for linear systems.
Zhongming Teng, Xuansheng Wang
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Lubricants, 2023 The complex sliding behavior inside ball bearings seriously affects the mechanical system’s performance. Current dynamic models for predicting this behavior suffer from poor generality and convergence.
Shuaijun Ma +5 more
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On the Convergence of a Kurchatov-Type Method for Solving Nonlinear Equations and Its Applications
AppliedMathA local and a semi-local convergence analysis are presented for the Kurchatov-type method to solve numerically nonlinear equations in a Banach space. The method depends on a real parameter. By specializing the parameter, we obtain methods already studied
Ioannis K. Argyros +2 more
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Mathematical Problems in Engineering, 2019 The main contribution of this study is to present a new optimal eighth‐order scheme for locating zeros with multiplicity m ≥ 1. An extensive convergence analysis is presented with the main theorem in order to demonstrate the optimal eighth‐order convergence of the proposed scheme.
Ramandeep Behl +3 more
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On Newton's method for subanalytic equations
Journal of Numerical Analysis and Approximation Theory, 2017 We present local and semilocal convergence results for Newton’s method in order to approximate solutions of subanalytic equations. The local convergence results are given under weaker conditions than in earlier studies such as [9], [10], [14], [15], [24]
Ioannis K. Argyros, Santhosh George
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Extending the Applicability of Newton’s Algorithm with Projections for Solving Generalized Equations
Applied System Innovation, 2020 A new technique is developed to extend the convergence ball of Newton’s algorithm with projections for solving generalized equations with constraints on the multidimensional Euclidean space. This goal is achieved by locating a more precise region than in
Michael I. Argyros +4 more
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