Related papers: On Josephy-Halley method for generalized equations
The present paper is concerned with the semilocal convergence problems of Halley's method for solving nonlinear operator equation in Banach space. Under some so-called majorant conditions, a new semilocal convergence analysis for Halley's…
In this paper we consider the Newton's method for solving the generalized equation of the form $ f(x) +F(x) \ni 0, $ where $f:{\Omega}\to Y$ is a continuously differentiable mapping, $X$ and $Y$ are Banach spaces, $\Omega\subseteq X$ an…
This paper develops an efficient iterative method for computing all zeros of solutions of second order ordinary differential equations. A third order Halleys method is first derived by approximating the solution of an associated Riccati…
Recently Ahmadi et al. (2021) and Tagliaferro (2022) proposed some iterative methods for the numerical solution of linear systems which, under the classical hypothesis of strict diagonal dominance, typically converge faster than the Jacobi…
First order shape optimization methods, in general, require a large number of iterations until they reach a locally optimal design. While higher order methods can significantly reduce the number of iterations, they exhibit only local…
In this paper we study Newton's method for solving the generalized equation $F(x)+T(x)\ni 0$ in Hilbert spaces, where $F$ is a Fr\'echet differentiable function and $T$ is set-valued and maximal monotone. We show that this method is local…
The use of second order information on the forward operator often comes at a very moderate additional computational price in the context of parameter identification probems for differential equation models. On the other hand the use of…
A new one-parameter family of iterative method for solving nonlinear equations is constructed and studied. Two variants, both with cubic convergence, are developed, one for finding simple zeros and other for multiple zeros of known…
This paper is concerned with a generalized Halanay inequality and its applications to fractional-order delay linear systems. First, based on a sub-semigroup property of Mittag-Leffler functions, a generalized Halanay inequality is…
Solving symmetric positive semidefinite linear systems is an essential task in many scientific computing problems. While Jacobi-type methods, including the classical Jacobi method and the weighted Jacobi method, exhibit simplicity in their…
We describe inexact proximal Newton-like methods for solving degenerate regularized optimization problems and for the broader problem of finding a zero of a generalized equation that is the sum of a continuous map and a maximal monotone…
In this paper we prove the global convergence of the complex Jacobi method for Hermitian matrices for a large class of generalized serial pivot strategies. For a given Hermitian matrix $A$ of order $n$ we find a constant $\gamma<1$…
We consider the Cauchy problem for the Gross-Pitaevskii infinite linear hierarchy of equations on $\mathbb{R}^n.$ By introducing a (F)-norm in certain Sobolev type spaces of sequences of marginal density matrices, we establish local…
We demonstrate a systematic method for solving the Hamilton-Jacobi equation for general relativity with the inclusion of matter fields. The generating functional is expanded in a series of spatial gradients. Each term is manifestly…
This paper considers the generalized continuation Newton method and thetrust-region updating strategy for the underdetermined system of nonlinear equations. Moreover, in order to improve its computational efficiency, the new method will not…
This paper demonstrates new methods and implementations of nonlinear solvers with higher-order of convergence, which is achieved by efficiently computing higher-order derivatives. Instead of computing full derivatives, which could be…
The Petviashvili's iteration method has been known as a rapidly converging numerical algorithm for obtaining fundamental solitary wave solutions of stationary scalar nonlinear wave equations with power-law nonlinearity: \ $-Mu+u^p=0$, where…
We give a new improvement over Newton's method for root-finding, when the function in question is doubly differentiable. It generally exhibits faster and more reliable convergence. It can be also be thought of as a correction to Halley's…
This work proposes a higher-order iterative framework for solving matrix equations, inspired by the structure and functionality of neural networks. A modification of the classical Jacobi iterative method is introduced to compute…
In this paper we consider a version of the Kantorovich's theorem for solving the generalized equation $F(x)+T(x)\ni 0$, where $F$ is a Fr\'echet derivative function and $T$ is a set-valued and maximal monotone acting between Hilbert spaces.…