Results 61 to 70 of about 2,871 (179)
Generalized Newton's Method based on Graphical Derivatives [PDF]
, 2010 This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical derivatives, which have
Hoheisel, T. +3 more
core +2 more sources
International Journal for Numerical Methods in Engineering, Volume 126, Issue 24, 30 December 2025.ABSTRACT This study presents a new optimized block hybrid method and spectral simple iteration method (OBHM‐SSIM) for solving nonlinear evolution equations. In this method, we employed a combination of the spectral collocation method in space and the optimized block hybrid method in time, along with a simple iteration scheme to linearize the equations.
Salma Ahmedai +4 more
wiley +1 more source
Multivariate Neural Network Operators: Simultaneous Approximation and Voronovskaja‐Type Theorem
Mathematical Methods in the Applied Sciences, Volume 48, Issue 11, Page 10669-10677, 30 July 2025.ABSTRACT In this paper, the simultaneous approximation and a Voronoskaja‐type theorem for the multivariate neural network operators of the Kantorovich type have been proved. In order to establish such results, a suitable multivariate Strang–Fix type condition has been assumed.
Marco Cantarini, Danilo Costarelli
wiley +1 more source
Using decomposition of the nonlinear operator for solving non‐differentiable problems
Mathematical Methods in the Applied Sciences, Volume 48, Issue 7, Page 7987-8006, 15 May 2025.Starting from the decomposition method for operators, we consider Newton‐like iterative processes for approximating solutions of nonlinear operators in Banach spaces. These iterative processes maintain the quadratic convergence of Newton's method.
Eva G. Villalba +3 more
wiley +1 more source
Neural‐network‐based regularization methods for inverse problems in imaging
GAMM-Mitteilungen, Volume 47, Issue 4, November 2024.Abstract This review provides an introduction to—and overview of—the current state of the art in neural‐network based regularization methods for inverse problems in imaging. It aims to introduce readers with a solid knowledge in applied mathematics and a basic understanding of neural networks to different concepts of applying neural networks for ...
Andreas Habring, Martin Holler
wiley +1 more source
One dimensional nonlinear integral operator with Newton–Kantorovich method
Journal of King Saud University - Science, 2016 AbstractThe Newton–Kantorovich method (NKM) is widely used to find approximate solutions for nonlinear problems that occur in many fields of applied mathematics. This method linearizes the problems and then attempts to solve the linear problems by generating a sequence of functions. In this study, we have applied NKM to Volterra-type nonlinear integral
Eshkuratov, Zainidin K. +2 more
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Solving Large‐Scale Unconstrained Optimization Problems with an Efficient Conjugate Gradient Class
Journal of Mathematics, Volume 2024, Issue 1, 2024.The main goal of this paper is to introduce an appropriate conjugate gradient class to solve unconstrained optimization problems. The presented class enjoys the benefits of having three free parameters, its directions are descent, and it can fulfill the Dai–Liao conjugacy condition.
Sanaz Bojari +2 more
wiley +1 more source
Improving Newton's method performance by parametrization: the case of Richards equation [PDF]
, 2016 The nonlinear systems obtained by discretizing degenerate parabolic equations may be hard to solve, especially with Newton's method. In this paper, we apply to Richards equation a strategy that consists in defining a new primary unknown for the ...
Brenner, Konstantin, Cancès, Clément
core +3 more sources
Newton-Kantorovich-Vietoris method
, 2017 In this short work we consider nonlinear equation in Banach space $x = A(x)$. We combine classical Newton method with Vietoris method to propose new more general method. Under rather general conditions about the noise we investigate local convergence of the method.
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Semilocal analysis of equations with smooth operators
International Journal of Mathematics and Mathematical Sciences, 1981 Recent work on semilocal analysis of nonlinear operator equations is informally reviewed. A refined version of the Kantorovich theorem for Newton's method, with new error bounds, is presented. Related topics are briefly surveyed.
George J. Miel
doaj +1 more source