On the fourth order root finding methods of Euler's type.
On the gap between the semilocal convergence domains of two Newton methods
We answer a question posed by Cianciaruso and De Pascale: What is the exact size of the gap between the semilocal convergence domains of the Newton and the modified Newton method? In particular, is it possible to close it? Our answer is yes in some cases. Using some ideas of ours and more precise error estimates we provide a semilocal convergence analysis for both methods with the following advantages over earlier approaches: weaker hypotheses; finer error bounds on the distances involved, and at...
On the Global Convergence of Halley's Iteration Formula.
On the guaranteed convergence of the Japanese zero-finding method.
On the hypoellipticity of pseudo-differential systems with a diagonal principal symbol
On the improved family of simultaneous methods for the inclusion of multiple polynomial zeros.
On the iterative process
On the Local Convergence of Certain Two Step Terative Procedures.
On the local convergence of Kung-Traub's two-point method and its dynamics
In this paper, the local convergence analysis of the family of Kung-Traub's two-point method and the convergence ball for this family are obtained and the dynamical behavior on quadratic and cubic polynomials of the resulting family is studied. We use complex dynamic tools to analyze their stability and show that the region of stable members of this family is vast. Numerical examples are also presented in this study. This method is compared with several widely used solution methods by solving test...
On the order of convergence of Broyden-Gay-Schnabel's method
On the possibility of calculation of zero points of solutions of differential equations of the second order
On the R-Order of Coupled Sequences Arising in Single-Step Type Methods.
On the semilocal convergence of a fast two-step Newton method.
On the shifted QR iteration applied to companion matrices.
On the Solutions to Polynomial Systems Obtained by Homotopy Methods.
On the Various Bisection Methods Derived from Vincent’s Theorem
In 2000 A. Alesina and M. Galuzzi presented Vincent’s theorem “from a modern point of view” along with two new bisection methods derived from it, B and C. Their profound understanding of Vincent’s theorem is responsible for simplicity — the characteristic property of these two methods. In this paper we compare the performance of these two new bisection methods — i.e. the time they take, as well as the number of intervals they examine in order to isolate the real roots of polynomials — against that...
One new kind of irregular spectra
Opérateurs invariants hypoelliptiques sur un groupe de Lie nilpotent
Opérateurs pseudo-différentiels et classes de Gevrey
Optimal fourth order family of iterative methods