Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=48889#.VDc0L1fHRK0 Author(s) Trevor M. O’Brien , Gareth E. Roberts Affiliation(s) Department of Computer Science, Brown University, Providence, USA . Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, USA . ABSTRACT Though well-known for its simplicity and efficiency, Newton’s method applied to a complex polynomial can fail quite miserably, even on a relatively large open set of initial guesses. In this work, we present some analytic and numerical results for Newton’s method applied to the complex quartic family where is a parameter. The symmetric location of the roots of allows for some easy reductions. In partic...
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