Third order convergence theorem for a family of Newton like methods in Banach space

In this paper, we propose a family of Newton-like methods in Banach space which includes some well known third-order methods as particular cases. We establish the Newton-Kantorovich type convergence theorem for a proposed family and get an error estimate

On the development and extensions of some classes of optimal three-point iterations for solving nonlinear equations

We develop a new families of optimal eight--order methods for solving nonlinear equations. We also extend some classes of optimal methods for any suitable choice of iteration parameter. Such development and extension was made using sufficient convergence conditions given in [14]. Numerical examples are considered to check the convergence order of new families and extensions of some well-known methods

Comparison of some optimal derivative-free three-point iterations

We show that the well-known Khattri et al. methods and Zheng et al. methods are identical. In passing, we propose a suitable calculation formula for Khattri et al. methods. We also show that the families of eighth-order derivative-free methods obtained in [8] include some existing methods, among them the above-mentioned ones as particular cases. We also give the sufficient convergence condition of these families. Numerical examples and comparison with some existing methods were made. In addition, the dynamical behavior of methods of these families is analyzed

Accelerating the convergence of Newton-type iterations

In this paper, we present a new accelerating procedure in order to speed up the convergence of Newton-type methods. In particular, we derive iterations with a high and optimal order of convergence. This technique can be applied to any iteration with a low order of convergence. As expected, the convergence of the proposed methods was remarkably fast. The effectiveness of this technique is illustrated by numerical experiments

Relationship between the inexact Newton method and the continuous analogy of Newton's method

In this paper we propose two new strategies to determine the forcing terms that allow one to improve the efficiency and robustness of the inexact Newton method. The choices are based on the relationship between the inexact Newton method and the continuous analogy of Newton's method. With the new forcing terms, the inexact Newton method is locally $Q$-superlinearly and quadratically convergent. Numerical results are presented to support the effectiveness of the new forcing terms

Mathematical Modeling of Boson-Fermion Stars in the Generalized Scalar-Tensor Theories of Gravity

A model of static boson-fermion star with spherical symmetry based on the scalar-tensor theory of gravity with massive dilaton field is investigated numerically. Since the radius of star is \textit{a priori} an unknown quantity, the corresponding boundary value problem (BVP) is treated as a nonlinear spectral problem with a free internal boundary. The Continuous Analogue of Newton Method (CANM) for solving this problem is applied. Information about basic geometric functions and the functions describing the matter fields, which build the star is obtained. In a physical point of view the main result is that the structure and properties of the star in presence of massive dilaton field depend essentially both of its fermionic and bosonic components.Comment: 16 pages, amstex, 5 figures, changed conten

Shell Model in the Complex Energy Plane

This work reviews foundations and applications of the complex-energy continuum shell model that provides a consistent many-body description of bound states, resonances, and scattering states. The model can be considered a quasi-stationary open quantum system extension of the standard configuration interaction approach for well-bound (closed) systems.Comment: Topical Review, J. Phys. G, Nucl. Part. Phys, in press (2008

Optimization by parameters in the iterative methods for solving non-linear equations

In this paper, we used the necessary optimality condition for parameters in a two-point iterations for solving nonlinear equations. Optimal values of these parameters fully coincide with those obtained in [6] and allow us to increase the convergence order of these iterative methods. Numerical experiments and the comparison of existing robust methods are included to confirm the theoretical results and high computational efficiency. In particular, we considered a variety of real life problems from different disciplines, e.g., Kepler’s equation of motion, Planck’s radiation law problem, in order to check the applicability and effectiveness of our proposed methods