Two Fourth-order Iterative Methods Based on Continued Fraction for Root-finding Problems

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.

Authors:

• Shengfeng Li
• Rujing Wang

Keywords:

• Iterative method
• Fixed-point iteration
• Thiele's continued fraction
• Order of convergence.

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