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 new exponential iterative formulae are effective and comparable to those of the well-known Newton and Steffensen methods.