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The test function is as follows see [ 10 ] :. The test results are listed in Table 1. The test function is as follows see [ 9 , 10 , 13 , 14 ] :. The test results are listed in Table 2.

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The test function is as follows see [ 4 ] :. The test results are listed in Table 3. The test function is as follows see [ 10 , 13 , 14 ] :. Consider the unrestraint optimum problem see [ 18 ]. Consider the discrete two-point boundary value problems see [ 19 ] :. From the seven examples in Section 4 , we can see that the newly developed method 42 - 43 has the advantages of fast convergence speed we can get from the CPU time , small number of iterations.

In a word, our method 42 - 43 is quite robust and effective.

Argyros , Hilout : Secant-like Method for Solving Generalized Equations

The authors declare that there is no conflict of interests regarding the publication of this paper. All authors contributed equally and significantly in writing this paper. All authors read and approved the final paper. National Center for Biotechnology Information , U. Journal List ScientificWorldJournal v. Published online Mar Author information Article notes Copyright and License information Disclaimer.

Received Feb 12; Accepted Feb Huang and C. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article has been cited by other articles in PMC. Abstract We present a fixed-point iterative method for solving systems of nonlinear equations. Algorithm 1 — Step 0 initialization.

Step 1 the predictor step. The n -Dimensional Case In this section, we consider the n -dimensional case of the method, and we also study these iterative methods' order of convergence. Algorithm 3 — Step 0 initialization. Numerical Examples In this section we present some examples to illustrate the efficiency and the performance of the newly developed method 42 - 43 present study HM. Open in a separate window.

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Conclusion From the seven examples in Section 4 , we can see that the newly developed method 42 - 43 has the advantages of fast convergence speed we can get from the CPU time , small number of iterations. Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper.

Fixed point iteration method - idea and example

Authors' Contribution All authors contributed equally and significantly in writing this paper. References 1. Nondiscrete Induction and Iterative Processes. Research Notes in Mathematics. Noor MA. Bezorgopties We bieden verschillende opties aan voor het bezorgen of ophalen van je bestelling. Welke opties voor jouw bestelling beschikbaar zijn, zie je bij het afronden van de bestelling.

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Convergence and Applications of Newton-type Iterations

Schrijf een review. E-mail deze pagina. Auteur: Ioannis K. Samenvatting This monograph is devoted to a comprehensive treatment of iterative methods for solving nonlinear equations with particular emphasis on semi-local convergence analysis.

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Theoretical results are applied to engineering, dynamic economic systems, input-output systems, nonlinear and linear differential equations, and optimization problems. Accompanied by many exercises, some with solutions, the book may be used as a supplementary text in the classroom for an advanced course on numerical functional analysis. Recensie s From the reviews: The book is devoted to iterative methods of approximative solving nonlinear operator equations The main part of the book deals with the classical Newton-Kantorovich method It may be used as a self-study reference or as a supplementary text for an advanced course in numerical functional analysis.

Convergence and Applications of Newton-type Iterations. Ioannis K. Newtonlike Methods. Variational Inequalities.