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This paper presents a comprehensive survey of methods which can be utilizedto search for solutions to systems of nonlinear equations (SNEs). Ourobjectives with this survey are to synthesize pertinent literature in thisfield by presenting a thorough description and analysis of the known methodscapable of finding one or many solutions to SNEs, and to assist interestedreaders seeking to identify solution techniques which are well suited forsolving the various classes of SNEs which one may encounter in real worldapplications.  To accomplish these objectives, we present a multi-part survey. In part one,we focus on root-finding approaches which can be used to search for solutionsto a SNE without transforming it into an optimization problem. In part two, wewill introduce the various transformations which have been utilized totransform a SNE into an optimization problem, and we discuss optimizationalgorithms which can then be used to search for solutions. In part three, wewill present a robust quantitative comparative analysis of methods capable ofsearching for solutions to SNEs.

Survey of Methods for Solving Systems of Nonlinear Equations, Part I: Root-finding Approaches