| 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 Words:
non-linear equation Thiele's continued fraction Viscovatov algorithm iterative method order of convergence
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| Fund Project: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). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2019.01.002 |
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