Results 11 to 20 of about 11,591,458 (275)
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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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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On a Convex Acceleration of Newton's Method [PDF]
, 1999 In this study, we use a convex acceleration of Newton's method (or super-Halley method) to approximate solutions of nonlinear equations. We provide sufficient convergence conditions for this method in three space settings: real line, complex plane, and ...
J. A. Ezquerro +5 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. +6 more
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J. Mach. Learn. Res., 2017 Many machine learning models involve solving optimization problems. Thus, it is important to deal with a large-scale optimization problem in big data applications. Recently, subsampled Newton methods have emerged to attract much attention due to their efficiency at each iteration, rectified a weakness in the ordinary Newton method of suffering a high ...
Ye, Haishan, Luo, Luo, Zhang, Zhihua
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Newton's method under weak Kantorovich conditions [PDF]
, 2000 The classical Kantorovich theorem on Newton's method assumes that the derivative of the operator involved satisfies a Lipschitz condition ∥F′(x) - F′(y)∥ ≤ L∥x - y∥. In this paper we weaken this condition, assuming that ∥F′(x) - F′(x 0)∥ ≤ L∥x - x 0∥ for
Gutiérrez, J.M. [0000-0002-0434-7250] +3 more
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, 2018 Capítulo del libro "Contemporary study of iterative methods: convergence, dynamics and applications"The center Lipschitz condition is used in this chapter, together with the Lipschitz condition, in order to obtain weaker convergence criteria to ensure ...
Argyros, Ioannis K +4 more
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An acceleration of Newton's method: Super-Halley method [PDF]
, 2001 From a study of the convexity we give an acceleration for Newton's method and obtain a new third order method. Then we use this method for solving non-linear equations in Banach spaces, establishing conditions on convergence, existence and uniqueness of ...
Gutiérrez, J.M. [0000-0002-0434-7250] +3 more
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Accelerated convergence in Newton's method for approximating square roots. [PDF]
, 2005 In this paper, we construct a modification of Newton's method to accelerate the convergence of this method to the approximation of the positive square root of a positive real number.
Romero, N. [0000-0002-0653-560X] +3 more
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