This paper presents an improvement to the recently-introduced factored method for the solution of nonlinear equations. The basic idea consists of transforming the original system by adding an offset to all unknowns. When searching for real solutions, a real offset prevents the intermediate values of unknowns from becoming complex. Reciprocally, when searching for complex solutions, a complex of...

We suggest and analyze a combination of a damped Newton’s method and a simplified version of Newton’s one. We show that the proposed iterations give two-sided approximations of the solution which can be efficiently used as posterior estimations. Some numerical examples illustrate the efficiency and performance of the method proposed. 2014 Published by Elsevier Inc.

The discretization of Gross-Pitaevskii equations (GPE) leads to a nonlinear eigenvalue problem with eigenvector nonlinearity (NEPv). We use two Newton-based methods compute the positive ground state GPE. first method comes from Newton-Noda iteration for saturable Schrödinger proposed by Ching-Sung Liu, which can be transferred GPE naturally. second combines idea root-finding and Newton method, ...

A new approach for distributed power load flow calculation using nonlinear equations is presented. This new approach, which is similar to the Newton Raphson’s simple method, uses an inverse Jacobian matrix of initial states for the iteration process. Moreover, nonlinear quadratic equations have been used as they are more appropriate for the distributed power load flow calculation. This paper de...

We develop general approximate Newton methods for solving Lips-chitz continuous equations by replacing the iteration matrix with a consistently approximated Jacobian thereby reducing the computation in the generalized Newton method. Locally superlinear convergence results are presented under moderate assumptions. To construct a consistently approximated Jacobian, we introduce two main methods: ...

Recently, the globally uniquely solvable (GUS) property of the linear transformation M ∈ Rn×n in the second-order cone linear complementarity problem (SOCLCP) receives much attention and has been studied substantially. Yang and Yuan [30] contributed a new characterization of the GUS property of the linear transformation, which is formulated by basic linear-algebra-related properties. In this pa...

The diffusion of dopants in silicon at high temperatures is modeled by a nonlinear parabolic system of partial differential equations on a twodimensional region with a moving boundary. A numerical solution using the L-stable TRBDF2 time integration method and a “box method” spatial discretization is described. Details are given of the methods used to specify and manipulate curves, and to define...

For any matrix automorphism group G associated with a bilinear or sesquilinear form, Mackey, Mackey, and Tisseur have recently shown that the matrix sign decomposition factors of A ∈ G also lie in G; moreover, the polar factors of A lie in G if the matrix of the underlying form is unitary. Groups satisfying the latter condition include the complex orthogonal, real and complex symplectic, and ps...

In this paper, we propose a regularized Newton method without line search. The proposed method controls a regularized parameter instead of a step size in order to guarantee the global convergence. We demonstrate that it is closely related to the TR-Newton method when the Hessian of the objective function is positive definite. Moreover, it does not solve nonconvex problems but linear equations a...

In this paper we have developed algorithms to solve macroeconometric models with forward-looking variables based on Newton method for nonlinear systems of equations. The most difficult step for Newton methods represents the resolution of a large linear system for each iteration. Thus, we compare the performances resulted by solving this linear system using two iterative methods and the direct m...