Some higher-order methods for the simultaneous approximation of multiple polynomial zeros

AbstractApplying Newton's and Halley's corrections, some modified methods of higher order for the simultaneous approximation of multiple zeros of a polynomial are derived. Further acceleration of convergence of these methods is performed by approximating all zeros in a serial fashion using the new approximations as they become available. Faster convergence is attained without additional calculations. Lower bounds of the R-order of convergence for the serial (single-step) methods are given