A new fourth-order convergent iterative method based on Thiele's continued fraction for solving equations

In this paper, we present a new one-step iterative method based on Thiele's continued fraction for solving non-linear equations. By applying the truncated Thiele's continued fraction twice, the iterative method is obtained. Analysis of convergence shows that the new method is fourth-order convergent. Numerical tests verifying the theory are given and based on the method, a new one-step iteration is developed. © 2011 Binary Information Press.