ERROR ANALYSIS OF k-FOLD PSEUDO-HALLEY S METHOD FINDING A SIMPLE ZERO

Given a nonlinear function f : R ! R that has a sim-ple real zero ？？, a new numerical method to be called k-fold pseudo-Halley s method is proposed and it s error analysis is under inves-tigation to con¯rm the convergence behavior near ？？. Under the assumption that f is su±ciently smooth in a small neighborhood of ？？, the order of convergence is found to be at least k+3. In addition, the corresponding asymptotic error constant is explicitly expressed in terms of k, ？？ and f as well as the derivatives of f. A zero-¯nding algorithm is written and has been successfully implemented for numerous examples with Mathematica.