Results 31 to 40 of about 1,893 (124)
On Newton‐Kantorovich Method for Solving the Nonlinear Operator Equation
Abstract and Applied Analysis, Volume 2015, Issue 1, 2015., 2015 We develop the Newton‐Kantorovich method to solve the system of 2 × 2 nonlinear Volterra integral equations where the unknown function is in logarithmic form. A new majorant function is introduced which leads to the increment of the convergence interval. The existence and uniqueness of approximate solution are proved and a numerical example is provided
Hameed Husam Hameed +4 more
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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
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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
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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
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Convergence Theorem for a Family of New Modified Halley’s Method in Banach Space
Journal of Applied Mathematics, Volume 2014, Issue 1, 2014., 2014 We establish convergence theorems of Newton‐Kantorovich type for a family of new modified Halley’s method in Banach space to solve nonlinear operator equations. We present the corresponding error estimate. To show the application of our theorems, two numerical examples are given.
Rongfei Lin +4 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
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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
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Extending the Newton–Kantorovich hypothesis for solving equations
, 2010 The famous Newton–Kantorovich hypothesis (Kantorovich and Akilov, 1982 [3], Argyros, 2007 [2], Argyros and Hilout, 2009 [7]) has been used for a long time as a sufficient condition for the convergence of Newton’s method to a solution of an equation in ...
Argyros, Ioannis K., Hilout, Saïd
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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] +1 more
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A Simple Proof of Duality Theorem for Monge-Kantorovich Problem [PDF]
, 2004 We give a simple proof of the duality theorem for the Monge-Kantorovich problem in the Euclidean setting.
Mikami, Toshio
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