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Algorithms 2016, 9(1), 2; doi:10.3390/a9010002

Offset-Assisted Factored Solution of Nonlinear Systems

Department of Electrical Engineering, University of Seville, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain
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Academic Editors: Alicia Cordero, Juan R. Torregrosa and Francisco I. Chicharro
Received: 31 October 2015 / Revised: 11 December 2015 / Accepted: 14 December 2015 / Published: 23 December 2015
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
View Full-Text   |   Download PDF [1775 KB, uploaded 23 December 2015]   |  

Abstract

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 offset is advisable to allow the iterative process to quickly abandon the real domain. Several examples are used to illustrate the performance of the proposed algorithm, when compared to Newton’s method. View Full-Text
Keywords: nonlinear systems; factored solution method; Newton’s method nonlinear systems; factored solution method; Newton’s method
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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

Ruiz-Oltra, J.M.; Gómez-Quiles, C.; Gómez-Expósito, A. Offset-Assisted Factored Solution of Nonlinear Systems. Algorithms 2016, 9, 2.

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