Lifting/descending processes for polynomial zeros
The 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 fur 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. (C) 2000 Academic Press.
polynomial zeros numerical splitting a polynomial into factors lifting polynomial zeros