In this chapter, we are primarily interested in the construction of computationally verifiable
initial conditions and the corresponding convergence analysis of the simultaneous methods …

We present an error analysis for two related quadrature methods (the Delves–Lyness
method and its modification by Kravanja, Sakurai and Van Barel) for computing all the zeros …

The numerical quotient-difference algorithm, or the qd-algorithm, can be used for
determining the poles of a meromorphic function directly from its Taylor coeffcients. We show …

Starting from a suitable fixed point relation, a new family of iterative methods for the
simultaneous inclusion of multiple complex zeros in circular complex arithmetic is …

In this paper we construct iterative methods of Ostrowski's type for the simultaneous
inclusion of all zeros of a polynomial. Using the concept of the R-order of convergence of …

In this paper, we give the convergence analysis of the Euler-like iterative method for the
simultaneous inclusion of all simple real or complex zeros of a polynomial. The established …

Higher-order methods for the simultaneous inclusion of complex zeros of algebraic
polynomials are presented in parallel (total-step) and serial (single-step) versions. If the …

Let n be a positive integer, let a_-n+ 1,..., a_-1, a_0, a_1,..., a_ n-1 be complex numbers and
let T:= a_ k-1 _ k, l= 0^ n-1 be a nonsingular n× n complex Toeplitz matrix. We present a …

A one parameter family of iterative methods for the simultaneous determination of all (simple
or multiple) complex zeros of a polynomial, based on a cubically convergent Hansen …

Using a suitable fixed point relation with a complex parameter, a new one parameter family
of simultaneous methods of the fourth order for finding complex zeros of a polynomial is …