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Journal of Numerical Analysis and Approximation Theory, 2007 In this study we are concerned with the problem of approximating a locally unique solution of an equation in a Banach space setting using Newton's and modified Newton's methods. We provide weaker convergence conditions for both methods than before [6]-[8]
Ioannis Argyros
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, 2016 In this chapter we study the convergence of Newton’s method for nonlinear equations and nonlinear inclusions in a Banach space. Nonlinear mappings, which appear in the right-hand side of the equations, are not necessarily differentiable. Our goal is to obtain an approximate solution in the presence of computational errors.
Maes, Chris
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Application of Newton’s method to solve optimization geodetic tasks [PDF]
E3S Web of Conferences, 2021 The article provides general information on nonlinear methods of programming. The algorithm for determining the minimum of various target functions by Newton’s method of the second order is considered.
Bykasov D. A. +2 more
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An investigation of Newton-Sketch and subsampled Newton methods [PDF]
Optimization Methods and Software, 2020 Sketching, a dimensionality reduction technique, has received much attention in the statistics community. In this paper, we study sketching in the context of Newton's method for solving finite-sum optimization problems in which the number of variables and data points are both large.
Albert S. Berahas +2 more
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CoRR, 2021 In this work, we present a program in the computational environment, GeoGebra, that enables a graphical study of Newton's Method. Using this computational device, we will analyze Newton's Method convergence applied to various examples of real functions. Then, it will be given a guide to the construction of the program in GeoGebra.
Orizon P. Ferreira, Davi A. Pires
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Современные информационные технологии и IT-образование, 2021 The proposed article examines the methodology for developing students' thinking flexibility by combining various approaches to the implementation of educational mathematical tasks.
Valeriy Sekovanov +3 more
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Современные информационные технологии и IT-образование, 2023 The proposed article describes the methodology for performing a multi-stage mathematical-informational task "Newton's Method for Complex Polynomials", aimed at developing the creative qualities of students.
Valeriy S. Sekovanov +4 more
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Multihomogeneous Newton methods [PDF]
Mathematics of Computation, 1999 We study multihomogeneous analytic functions and a multihomogeneous Newton’s method for finding their zeros. We give a convergence result for this iteration and we study two examples: the evaluation map and the generalized eigenvalue problem.
Jean-Pierre Dedieu, Mike Shub
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Approach to development of algorithms of Newtonian methods of unconstrained optimization, their software implementation and benchmarking [PDF]
Компьютерные исследования и моделирование, 2013 The approach to increase efficiency of Gill and Murray's algorithm of Newtonian methods of unconstrained optimization with step adjustment creation is offered, rests on Choleskys factorization.
Gennadiy Anatolievich Zelenkov +1 more
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Convergence of the relaxed Newton's method [PDF]
, 2014 In this work we study the local and semilocal convergence of the relaxed Newton's method, that is Newton's method with a relaxation parameter 0 < λ < 2.
Argyros, I.K. +3 more
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