In this paper, we present a new fourth-order modification of Newton’s method for multiple roots, which is based on existing second -order. Modification of Newton’s multiple root-finding methods. Some numerical examples illustrate that the new method is more efficient and performs better than other methods for multiple roots.

We study an infeasible interior path-following method for complemen-tarity problems. The method uses a wide neighborhood and takes one or two Newton steps per iteration. We show that the method attains global convergence, assuming the iterates are deened and bounded (which occurs when the function is a P 0-R 0-function or when the function is monotone and a suuciently positive solution exists)....

In the study of transverse vibrations of a hinged beam there arises a boundary value problem for fourth order ordinary differential equation, where a significant difficulty lies in a nonlinear term under integral sign. In recent years several authors considered finite approximation of the problem and proposed an iterative method for solving the system of nonlinear equations obtained. The essenc...

Newton’s method is one of the most famous numerical methods. Its origins, as the name suggests, lies in part with Newton, but the form familiar to us today is due to Simpson of “Simpson’s Rule” fame. Originally proposed to find the roots of polynomials it was Simpson who proposed using it for general nonlinear equations and for its use in optimization by finding a root of the gradient. Here we ...

PAD&APPROXIMANTS FOR THE SOLUTION OF A SYTEM OF NONLINEAR EQUATIONS ANNIE Cm-T? and PAUL VAN DER CRUYSSEN University of Antwerp, Department of Mathematics, Universiteitsplein 1, B-2610 Wihijk, Belgium (Receioed January 1981; and in revised form May 1982) Communicated by J. F. Traub Abstract-Let F: R4 *R’ and let x* be a simple root of the system of nonlinear equations F(x) = 0. We will construc...

We try to arm Newton’s iteration for univariate polynomial factorization with greater convergence power by shifting to a larger basic system of multivariate constraints. The convolution equation is a natural means for a desired expansion of the basis for this iteration versus the classical univariate method, which is more vulnerable to foreign distractions from its convergence course. Compared ...

1 Student of Department of Electronics & Communication Engineering, 2 Professor, Department of Mathematics, 1,2 R. V. College of Engineering, Mysore Road, Bangalore, Karnataka-560 059, INDIA __________________________________________________________________________________________ Abstract: New iterative algorithms for finding the nth root of a positive number m, to any degree of accuracy, are ...