in this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. each of them requires one evaluation of the function and two of its first derivative per iteration. several numerical examples are given to illustrate the performance of the presented methods.

Starting from a suitable fixed point relation and employing Schröder’s and Halley-like corrections, we derive some high order iterative methods for the simultaneous inclusion of polynomial multiple zeros in circular complex interval arithmetic. These methods are more efficient compared to the existing inclusion methods based on fixed point relations. Using the concept of the R-order of converge...

We consider piecewise polynomial approximation of order M in N-dimensions with a tensor product partition of the space. We assume that the partition is to be chosen to minimize ------'the-maximum----em>r---in-the-approximation.------1be---optimal---Iate---gf--cgrwetgence-foyieGeWisef--------polynomial approximation to a smooth function for unconstrained partitions is known to be order ~/N where...

In this paper, we present a new iterative method with order of convergence eighth for solving nonlinear equations. Periteration this method requires three evaluations of the function and one evaluation of its first derivative. A general error analysis providing the eighth order of convergence is given. Several numerical examples are given to illustrate the efficiency and performance of the new ...

A new modified method ISS for the simultaneous bounding all the zeros of a polynomial is formulated in this paper. The efficiency of this method is measured on the CPU times and the number of iterations after satisfying the convergence criteria where the results are obtained using five tested polynomials. The R-order of convergence of this method is at least 9. Mathematics Subject Classificatio...

The interval version of the complex third-order method of Maehly, Borsch-Supan, Ehrlich, and Aberth is the most efficient method for simultaneous inclusion of simple polynomial roots [14]. In this note, Gargantini’s generalization of this third-order interval method for multiple roots is accelerated using Schroder’s modification of Newton’s corrections and modifying the required interval invers...

in this article, we propose and analyze a computational method for numerical solution of general two point boundary value problems. method is tested on problems to ensure the computational eciency. we have compared numerical results with results obtained by other method in literature. we conclude that propose method is computationally ecient and eective.

This paper studies the vector optimization problem of finding weakly efficient points for maps from R to R, with respect to the partial order induced by a closed, convex, and pointed cone C ⊂ R, with nonempty interior. We develop for this problem an extension of the proximal point method for scalar-valued convex optimization problem with a modified convergence sensing conditon that allows us to...

Relational Bayesian networks are an extension of the method of probabilistic model construction by Bayes-ian networks. They deene probability distributions on nite relational structures by conditioning the probability of a ground atom r(a 1 ; : : : ; a n) on rst-order properties of a 1 ; : : : ; a n that have been established by previous random decisions. In this paper we investigate from a nit...