On convergence behavior of an iterative method for finding polynomial factors of analytic functions

摘要

Convergence properties of an iterative method for evaluating the coefficients of a monic factor of a power series f(z) are considered. A factoring method that finds a polynomial factor of f(z) does not need to separate simple zeros from a cluster of the zeros of f(z), therefore it is useful for the case that f(z) has multiple or close zeros. By providing a matrix presentation of the factoring method we derive some theoretical results about convergence behavior. Some examples illustrate properties of the method numerically.