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Erratum published on 12 May 2017, see Algorithms 2017, 10(2), 55.

Open AccessArticle
Algorithms 2017, 10(1), 17; doi:10.3390/a10010017

A Preconditioned Iterative Method for Solving Systems of Nonlinear Equations Having Unknown Multiplicity

1
Dipartimento di Scienza e Alta Tecnologia, Universita dell’Insubria, Via Valleggio 11, Como 22100, Italy
2
Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Eduard Maristanu 10, Barcelona 08019, Spain
3
UCERD (Pvt) Ltd, Islamabad 44000, Pakistan
4
Department of Computer Science, University of Gujrat, Gujrat 50700, Pakistan
5
Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
6
Heat and Mass Transfer Technological Center, Technical University of Catalonia, Colom 11, Terrassa 08222, Spain
7
Department of Mathematics, Government College University Lahore, Lahore 54000, Pakistan
*
Author to whom correspondence should be addressed.
Academic Editor: Alicia Cordero
Received: 13 November 2016 / Revised: 24 December 2016 / Accepted: 13 January 2017 / Published: 18 January 2017
View Full-Text   |   Download PDF [245 KB, uploaded 16 May 2017]

Abstract

A modification to an existing iterative method for computing zeros with unknown multiplicities of nonlinear equations or a system of nonlinear equations is presented. We introduce preconditioners to nonlinear equations or a system of nonlinear equations and their corresponding Jacobians. The inclusion of preconditioners provides numerical stability and accuracy. The different selection of preconditioner offers a family of iterative methods. We modified an existing method in a way that we do not alter its inherited quadratic convergence. Numerical simulations confirm the quadratic convergence of the preconditioned iterative method. The influence of preconditioners is clearly reflected in the numerically achieved accuracy of computed solutions. View Full-Text
Keywords: nonlinear equations; systems of nonlinear equations; singular Jacobian; roots with unknown multiplicity; nonlinear preconditioners; auxiliary function nonlinear equations; systems of nonlinear equations; singular Jacobian; roots with unknown multiplicity; nonlinear preconditioners; auxiliary function
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. (CC BY 4.0).

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MDPI and ACS Style

Ahmad, F.; Bhutta, T.A.; Shoaib, U.; Zaka Ullah, M.; Alshomrani, A.S.; Ahmad, S.; Ahmad, S. A Preconditioned Iterative Method for Solving Systems of Nonlinear Equations Having Unknown Multiplicity. Algorithms 2017, 10, 17.

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