%0 Journal Article %A Shengfeng Li and Rujing Wang %D 2011 %J International Journal of Mathematical and Computational Sciences %B World Academy of Science, Engineering and Technology %I Open Science Index 60, 2011 %T Two Fourth-order Iterative Methods Based on Continued Fraction for Root-finding Problems %U https://publications.waset.org/pdf/1449 %V 60 %X In this paper, we present two new one-step iterative methods based on Thiele-s continued fraction for solving nonlinear equations. By applying the truncated Thiele-s continued fraction twice, the iterative methods are obtained respectively. Analysis of convergence shows that the new methods are fourth-order convergent. Numerical tests verifying the theory are given and based on the methods, two new one-step iterations are developed. %P 1973 - 1976