Iterative methods for multiple zeros of a polynomial by clustering

摘要

For the numerical determination of zeros of a complex polynomial by simultaneous iterative methods, we show theorems on the fact that the approximations for a multiple zero gather around the exact zero when they become close approximations. Application of our theorems makes it possible to estimate the multiplicity of zeros dynamically as well as to improve the convergence to multiple zeros for the known methods, e.g. Durand-Kerner's or Tanabe's methods.