The guaranteed convergence of Laguerre-like method
The authors continue their study of a Laguerre-like method for the simultaneous computation of all zeros of polynomial. The method, recently presented by the first author [J. Comput. Appl. Math. 152, No. 1--2, 451--465 (2003; Zbl 1022.65053)], is recalled together with estimates and inequalities necessary for the convergence analysis. The main result of the paper is a theorem which gives a condition assuring fourth order convergence when the Laguerre-like method is applied to a polynomial of degree \(\geq 3\) with simple zeros. A numerical example of the method is given at the end of the paper.
scientific article; zbMATH DE number 2082581
scientific article