We investigate the parameter plane of the Newton's method applied to the family of quartic polynomials p a , b ( z ) = z 4 + a z 3 + b z 2 + a z + 1 , where a and b are real parameters. We divide the parameter plane ( a , b ) ź R 2 into twelve open and connected regions where p, p' and p'' have simple roots. In each of these regions we focus on the study of the Newton's operator acting on the Riemann sphere.
['B. Campos', 'Antonio Garijo', 'Xavier Jarque', 'P. Vindel']
Newton method for symmetric quartic polynomial