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Open AccessArticle

Offset-Assisted Factored Solution of Nonlinear Systems

Department of Electrical Engineering, University of Seville, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain
Author to whom correspondence should be addressed.
Academic Editors: Alicia Cordero, Juan R. Torregrosa and Francisco I. Chicharro
Algorithms 2016, 9(1), 2;
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)
PDF [1775 KB, uploaded 23 December 2015]


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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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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