Three-Stage Variable-Shift Iteration for Polynomial Zeros and Its Relation to Generalized Rayleigh Iteration

摘要

The report describes a new three-stage process for calculating the zeros of a polynomial with complex coefficients. The algorithm is similar in spirit to the two-stage algorithms studied by Traub in a series of papers. The algorithm is restriction free, that is, it converges for any distribution of zeros. A proof of global convergence is given. (Author)