Results 1 to 10 of about 360 (203)
CONVERGENCE OF THE RELAXED NEWTON'S METHOD [PDF]
Journal of the Korean Mathematical Society, 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. We give a Kantorovich-like theorem that can be applied for operators defined between two Banach spaces.
Argyros, I.K. +3 more
openaire +6 more sources
Attracting cycles for the relaxed Newton’s method [PDF]
Journal of Computational and Applied Mathematics, 2011 We study the relaxed Newton's method applied to polynomials.
Sergio Plaza, Natalia Romero
openaire +6 more sources
Buildings, 2023 The large-span, relaxed antenna network is a large deformation flexible structure due to its low pre-tension level of the wires. Its dynamic analysis under a wind load belongs to dynamic and geometric nonlinear problems, which is very complex to ...
Kai Qin +4 more
doaj +1 more source
Mathematics, 2021 The aim of this paper is to study, from a topological and geometrical point of view, the iteration map obtained by the application of iterative methods (Newton or relaxed Newton’s method) to a polynomial equation.
José Ignacio Extreminana-Aldana +3 more
doaj +1 more source
On the equivalence of dynamic relaxation and the Newton‐Raphson method [PDF]
International Journal for Numerical Methods in Engineering, 2017 SummaryDynamic relaxation is an iterative method to solve nonlinear systems of equations, which is frequently used for form finding and analysis of structures that undergo large displacements. It is based on the solution of a fictitious dynamic problem where the vibrations of the structure are traced by means of a time integration scheme until a static
Jef Rombouts +3 more
openaire +4 more sources
Relaxed Gauss--Newton Methods with Applications to Electrical Impedance Tomography [PDF]
SIAM Journal on Imaging Sciences, 2020 As second-order methods, Gauss--Newton-type methods can be more effective than first-order methods for the solution of nonsmooth optimization problems with expensive-to-evaluate smooth components. Such methods, however, often do not converge. Motivated by nonlinear inverse problems with nonsmooth regularization, we propose a new Gauss--Newton-type ...
Jyrki Jauhiainen +3 more
openaire +2 more sources
Random Iterations of Subhyperbolic Relaxed Newton's Methods [PDF]
, 2022 The family of the natural iterations of a subhyperbolic relaxed Newton s method of a complex polynomial devides the Riemann sphere into two disjoint sets: the nonempty, perfect, nowhere dense, connected and locally connected Julia set with Lebesgue measure zero, and the open Fatou set with stable simply connected components.
Arghanoun, Ghazaleh +4 more
openaire +2 more sources
Holomorphic motions in the parameter space for the relaxed Newton's method. [PDF]
Kodai Mathematical Journal, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +2 more sources
Relaxing Convergence Conditions for Newton's Method
Journal of Mathematical Analysis and Applications, 2000 The classical Kantorovich theorem on Newton's method assumes that the first derivative of the operator involved satisfies a Lipschitz condition ∥Γ0[F′(x)-F′(y)]∥≤L∥x-y∥. In this paper, we weaken this condition, assuming that ∥Γ0[F′(x)-F′(x0)]∥≤ω(∥x-x0∥) for a given point x0. © 2000 Academic Press.
openaire +4 more sources
A relaxed generalized Newton iteration method for generalized absolute value equations
AIMS Mathematics, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yang Cao, Quan Shi, Sen-Lai Zhu
openaire +3 more sources