Inverse power and Durand-Kerner iterations for univariate polynomial root-finding
The paper is devoted to the study of a special class of iterative methods for simultaneous approximations of all roots of a given polynomial, known as Weierstrass (Durand-Kerner), briefly W(D-K), iterations. After a unifying derivation of the W(D-K) algorithm and its higher-order extensions (in Section 2) and some considerations regarding the choice of initial approximations, when applying these methods (Section 3), the rest of the paper focusses on the inverse power method for finding the eigenvalues of a generalized companion matrix of a polynomial. This is an alternative approach to root finding, based on the fact that the method for finding all roots reduces to the corresponding problem of computing all eigenvalues of the companion matrix. Numerical experiments are also considered in order to show the effectiveness of the algorithms.
scientific article; zbMATH DE number 2075472
scientific article