Lifting/Descending Processes for Polynomial Zeros

AbstractThe recently proposed Chebyshev-like lifting map for the zeros of a univariate polynomial was motivated by its applications to splitting a univariate polynomial p(z) numerically into factors, which is a major step of some most efficient 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 Graeffe's lifting/descending process, and generalize lifting from Graeffe's and Chebyshev-like maps to any fixed rational map of the zeros of the input polynomial