Abstract
This paper gives a new iterative method to solve the non-linear equation. We prove that this method has the asymptotic convergent order 1 + \( \sqrt 3 \). When the iterative times exceed 2, only one evaluation of the function and one of its first derivative is required by each iteration of the method. Therefore the new method is better than Newton’s method.
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References
Ostrowski A M. Solution of Equations in Euclidean and Banach Space[M]. 3rd Ed. New York: Academic Press, 1973.
Weerakoon S, Fernando T G I. A variant of Newton’s method with accelerated third-order convergence[J]. Applied Mathematics Letters, 2000, 13: 87–93.
Özban A Y. Some new variants of Newton’s method[J]. Appl Math Lett, 2004, 17: 677–682.
Frontini M, Sormani E. Some variant of Newton’s method with third-order convergence[J]. Appl Math Comput, 2003, 140: 419–426.
Argyros I K, Chen D, Qian Q. The Jarratt method in Banach space setting[J]. J Comput Appl Math, 1994, 51: 103–106.
Ioannis K, Argyro S. A new iterative method of asymptotic order 1 + \( \sqrt 2 \) for the computation of fixed points[J]. International Journal of Computer Mathematics, 2005, 82(11): 1413–1428.
Chun Changbum. Some improvements of Jarratt’s method with sixth-order convergence[J]. Applied Mathematics and Computation, 2007, 90: 1432–1437.
Jbilou K, Sadok H. Vector extrapolation methods: Applications and numerical comparison[J]. Journal of Computational and Applied Mathematics, 2000, 122: 149–165.
Sidi A, Ford W F, Smith D A. Acceleration of convergence of vector sequences[J]. SIAM J Numer Anal, 1986, 23: 178–196.
Cabay S, Jackson L W. A polynomial extrapolation method for finding limits and antilimits for vector sequences[J]. SIAM J Numer Anal, 1976, 13: 734–752.
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Foundation item: Supported by the National Natural Science Foundation of China (10826082), the Key Disciplines Project of Shanghai Municipality (S30104) and the Shanghai Leading Academic Discipline Project (J50101)
Biography: WANG Xiuhua, female, Lecturer, research direction: numerical methods for non-linear problems.
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Wang, X., Tang, L. & Kou, J. A high-order newton-like method. Wuhan Univ. J. Nat. Sci. 16, 4–6 (2011). https://doi.org/10.1007/s11859-011-0701-7
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DOI: https://doi.org/10.1007/s11859-011-0701-7