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The Dynamics of Newton's Method on Complex Quartic Polynomial | ||
| journal of the college of basic education | ||
| Article 1, Volume 17, Issue 71, 2011, Pages 81-94 | ||
| Author | ||
| Dr.Hussein Jaber Abdul Hussein | ||
| Abstract | ||
| Newton's method is used to calculate approximately the roots of any complex or real valued function consists iteration. For each complex polynomial , Newton's method defines a dynamical system on the complex Riemann sphere.The our goal is to prove that any quartic polynomial with at least two distant roots topologically conjugate to and any two polynomials with roots has a similar quartic shape then the Newton function for each polynomial are conjugate. Finally ,we study the symmetry of Newton's function with real and complex axis. The software MatLab will use to view the dynamics of quartic polynomial after the iterations of Newton's method. The graphical nature of the iterations gave us very nice properties that allow us to describe the behavior of the points in the plane. | ||
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