Solving Nonlinear Equations

@article{Hornberger2013SolvingNE,
  title={Solving Nonlinear Equations},
  author={George M. Hornberger and Patricia L. Wiberg},
  journal={Advanced Optimization for Process Systems Engineering},
  year={2013}
}
  • G. Hornberger, P. Wiberg
  • Published 27 March 2013
  • Mathematics
  • Advanced Optimization for Process Systems Engineering
. The paper is devoted to the study of a system of nonlinear integral equations. First, this system is reduced to a fi xed point problem of a nonlinear integral operator and hence we can give suitable assumptions and using a fi xed point theorem of Krasnosel’skii type in order to obtain the existence of solutions. Next, we prove the existence of asymptotically stable solutions for the above system. In order to illustrate the results, an example is also presented. 
View via Publisher
relate.cs.illinois.edu
31 Citations
Background Citations
2
Methods Citations
4

31 Citations

Regularization path-following methods with the trust-region updating strategy for linear complementarity problems
In this article, we consider the regularization path-following method with the trust-region updating strategy for the linear complementarity problem. Moreover, we prove the global convergence of the…
Probabilistic learning constrained by realizations using a weak formulation of Fourier transform of probability measures
This paper deals with the taking into account a given set of realizations as constraints in the Kullback-Leibler minimum principle, which is used as a probabilistic learning algorithm. This permits…
Probabilistic learning inference of boundary value problem with uncertainties based on Kullback-Leibler divergence under implicit constraints
  • Christian Soize
  • Computer Science, Mathematics
    Computer Methods in Applied Mechanics and Engineering
  • 2022
Global monotone convergence of Newton-like iteration for a nonlinear eigen-problem
TLDR
It is shown that, starting from a multiple of the positive eigenvector of A, the Newton-like iteration for this nonlinear eigen-problem Ax+ F(x) = λx converges monotonically.
On convergence properties of the modified trust region method under Hölderian error bound condition
Trust region method is one of the important methods for nonlinear equations. In this paper, we show that the modified trust region method converges globally under the Hölderian continuity of the…
Quasi-genetic algorithms and continuation Newton methods with deflation techniques for global optimization problems
TLDR
Numerical results show that the proposed method is quite reliable to find the global optimal point of the unconstrained optimization problem, compared to the multi-start method (the built-in subroutine GlobalSearch.m of the MATLAB R2020a environment).
Continuation Newton methods with deflation techniques and  quasi-genetic evolution for global optimization problems
TLDR
Numerical results show that the proposed continuation Newton method with the deflation technique performs well for the large-scale global optimization problems, especially the problems of which are difficult to be solved by the known global optimization methods.
Generalized continuation Newton methods and the trust-region updating strategy for the underdetermined system
TLDR
The generalized continuation Newton method and the trust-region updating strategy for the underdetermined system of nonlinear equations is considered and is shown to be more robust and faster than the traditional optimization method such as the Levenberg-Marquardt method.
Extended Local Convergence for High Order Schemes Under ω-Continuity Conditions
Gus Argyros, Michael Argyros, Ioannis K. Argyros, Santhosh George Department of Computing and Technology, Cameron University, Lawton, Oklahoma, USA Department of Computing and Technology, Cameron…
Some Properties and Distribution of the Zeros of the q-Sigmoid Polynomials
The sigmoid polynomials combining - numbers and various properties of their polynomials are thoroughly presented in this paper. Based on several properties of - numbers, we derive some identities of…
...
...