A hybrid method for polynomial complex zero
The paper deals with an iterative algorithm for finding isolated simple complex zeroes of a polynomial. Using Weierstrass' interval formula for the simultaneous inclusion of all zeroes of the polynomial and rectangular floating-point arithmetic, a hybrid method with high computational efficiency is presented. Furthermore, error bounds of the approximate solution are determined. In a second part, a computationally verifiable test for the existence of a zero in a given disc is established. A numerical example is given, too.
scientific article; zbMATH DE number 4195053
scientific article