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Unconstrained convex optimization problems have enormous applications in various field of science and engineering. Different iterative methods are available in literature to solve such problem, and Newton method is among the oldest and…

Optimization and Control · Mathematics 2023-11-10 Santoshi Subhalaxmi Ray , Manideepa Saha

This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…

Optimization and Control · Mathematics 2026-03-03 Pham Duy Khanh , Boris S. Mordukhovich , Vo Thanh Phat

The prime objective of this paper is to design a new family of eighth-order iterative methods by accelerating the order of convergence and efficiency index of well existing seventh-order iterative method of \cite{Soleymani1} without using…

Numerical Analysis · Mathematics 2014-03-28 Anuradha Singh , J. P. Jaiswal

In this paper, we present a new modified Newton method a use of Haar wavelet formula for solving non-linear equations. This new method do not require the use of the second-order derivative. It is shown that the new method has third-order of…

Numerical Analysis · Mathematics 2017-01-03 Bijaya Mishra , Ambit Kumar Pany , Salila Dutta

We discuss a recursive family of iterative methods for the numerical approximation of roots of nonlinear functions in one variable. These methods are based on Newton-Cotes closed quadrature rules. We prove that when a quadrature rule with…

Numerical Analysis · Mathematics 2014-09-10 Mario M. Graça , Pedro M. Lima

There are thousands of papers on rootfinding for nonlinear scalar equations. Here is one more, to talk about an apparently new method, which I call ``Inverse Cubic Iteration'' (ICI) in analogy to the Inverse Quadratic Iteration in Richard…

Numerical Analysis · Mathematics 2020-07-15 Robert M. Corless

In this paper we derive a Newton type method to solve the non-linear system formed by combining the Tikhonov normal equations and Morozov's discrepancy principle. We prove that by placing a bound on the step size of the Newton iterations…

Numerical Analysis · Mathematics 2018-09-06 Nick Schenkels , Wim Vanroose

This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting…

Mathematical Software · Computer Science 2022-08-19 Ilias S. Kotsireas , Panos M. Pardalos , Alexander Semenov , William T. Trevena , Michael N. Vrahatis

In this paper, we consider the problem of solving a constrained system of nonlinear equations. We propose an algorithm based on a combination of the Newton and conditional gradient methods, and establish its local convergence analysis. Our…

Optimization and Control · Mathematics 2016-08-25 Max L. N. Goncalves , Jefferson G. Melo

We present an iterative root finding method for harmonic mappings in the complex plane, which is a generalization of Newton's method for analytic functions. The complex formulation of the method allows an analysis in a complex variables…

Complex Variables · Mathematics 2020-10-26 Olivier Sète , Jan Zur

We develop a randomized Newton's method for solving differential equations, based on a fully connected neural network discretization. In particular, the randomized Newton's method randomly chooses equations from the overdetermined nonlinear…

Numerical Analysis · Mathematics 2019-12-09 Qipin Chen , Wenrui Hao

This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first…

Optimization and Control · Mathematics 2023-01-24 Nicolas F. Armijo , Yunier Bello-Cruz , Gabriel Haeser

Functional iterations such as Newton's are a popular tool for polynomial root-finding. We consider realistic situation where some (e.g., better-conditioned) roots have already been approximated and where further computations is directed to…

Numerical Analysis · Mathematics 2019-07-09 Remi Imbach , Victor Y. Pan , Chee Yap , Ilias S. Kotsireas , Vitaly Zaderman

We describe a three precision variant of Newton's method for nonlinear equations. We evaluate the nonlinear residual in double precision, store the Jacobian matrix in single precision, and solve the equation for the Newton step with…

Numerical Analysis · Mathematics 2023-10-11 C. T. Kelley

The present author recently proposed and proved a relationship theorem between nonlinear polynomial equations and the corresponding Jacobian matrix. By using this theorem, this paper derives a Newton iterative formula without requiring the…

Computational Engineering, Finance, and Science · Computer Science 2024-09-21 W. Chen

In this paper, we propose a globally convergent method for solving constrained nonlinear systems. The method combines an efficient Newton conditional gradient method with a derivative-free and nonmonotone linesearch strategy. The global…

Optimization and Control · Mathematics 2018-06-06 M. L. N. Gonçalves , F. R. Oliveira

The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…

Numerical Analysis · Mathematics 2024-04-25 A. Torres-Hernandez , F. Brambila-Paz

Fixed-point or Newton-methods are typically employed for the numerical solution of nonlinear systems arising from discretization of nonlinear magnetic field problems. We here discuss an alternative strategy which uses local Quasi-Newton…

Numerical Analysis · Mathematics 2024-09-11 Herbert Egger , Felix Engertsberger , Lukas Domenig , Klaus Roppert , Manfred Kaltenbacher

We are concerned with the tensor equations whose coefficient tensor is an M-tensor. We first propose a Newton method for solving the equation with a positive constant term and establish its global and quadratic convergence. Then we extend…

Optimization and Control · Mathematics 2021-01-28 Dong-Hui Li Jie-Feng Xu , Hong-Bo Guan

A new method of root finding is formulated that uses a numerical iterative process involving three points. A given function y = f(x) whose roots are desired is fitted and approximated by a polynomial function of the form P(x)= a(x-b)^N that…

Numerical Analysis · Mathematics 2013-02-11 Ababu Teklemariam Tiruneh , William N. Ndlela , Stanley J. Nkambule