A Fourth-Order Convergent Iterative Method by Means of Thiele's Continued Fraction for Root-Finding Problem
Received:April 04, 2018  Revised:August 12, 2018
Key Word: non-linear equation   Thiele's continued fraction   Viscovatov algorithm   iterative method   order of convergence  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11571071), the Natural Science Key Foundation of Education Department of Anhui Province (Grant No.KJ2013A183), the Project of Leading Talent Introduction and Cultivation in Colleges and Universities of Education Department of Anhui Province (Grant No.gxfxZD2016270) and the Incubation Project of the National Scientific Research Foundation of Bengbu University (Grant No.2018GJPY04).
Author NameAffiliation
Shengfeng LI Institute of Applied Mathematics, Bengbu University, Anhui 233030, P. R. China 
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      In this paper, we propose a new single-step iterative method for solving non-linear equations in a variable. This iterative method is derived by using the approximation formula of truncated Thiele's continued fraction. Analysis of convergence shows that the order of convergence of the introduced iterative method for a simple root is four. To illustrate the efficiency and performance of the proposed method we give some numerical examples.
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