A new family of exponential iteration methods with quadratic convergence of both diameters and points for enclosing zeros of nonlinear equations
This paper presents a new class of exponential iteration methods with global convergence for finding a simple root x* of a nonlinear equation f (x) = 0 in the interval [a, b]. The new methods are shown to be quadratically convergent. Both the sequences of diameters {b(n) - a(n)} and the iterative sequence {x(n) - x*} are quadratically convergent to zero. The theoretical analysis and numerical experiments show that Dew exponential iterative formulae are effective and comparable to those of the well-known Newton and Steffensen methods. (c) 2006 Elsevier Ltd. All rights reserved.
quadratic convergence nonlinear equations global convergence exponential iterative formulae bisection method