Lifting/Descending Processes for Polynomial Zeros

The recently proposed Chebyshev-like lifting map for the zeros of a uni-variate polynomial was motivated by its applications to splitting a univariate polynomial p(x) numerically into factors, which is a major step of some most eeective algorithms for approximating polynomial zeros. We complement the Chebyshev-like lifting process by a descending process, decrease the estimated computational cost of performing the algorithm, demonstrate its correlation to Graeee's lifting/descending process and generalize lifting from Graeee's and Chebyshev-like maps to any xed rational map of the zeros of the input polynomial .