Balanced convergence of iterative methods to a multiple zero of a complex polynomial

@inproceedings{Miyakoda1992BalancedCO,
  title={Balanced convergence of iterative methods to a multiple zero of a complex polynomial},
  author={Tsuyako Miyakoda},
  year={1992}
}
Abstract We deal with the Durand-Kerner iterative method for a complex polynomial equation having multiple zeros. We will give the detailed proofs that the Durand-Kerner approximations to a multiple zero locate equidistant points on a sufficiently small circle when they are close to the exact zeros, and furthermore that the Durand-Kerner mapping, whose definition is given in the present paper, is contractive. This fact supports the balanced convergence of iteration observed in the author's… CONTINUE READING