Ball convergence theorems for eighth-order variants of Newton’s method under weak conditions
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- 作者：Ioannis K. Argyros ; Santhosh George
- 关键词：65D10 ; 65D99
- 刊名：Arabian Journal of Mathematics
- 出版年：2015
- 出版时间：June 2015
- 年：2015
- 卷：4
- 期：2
- 页码：81-90
- 全文大小：644 KB
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Santhosh George (2)
1. Department of Mathematical Sciences, Cameron University, Lawton, OK, 73505, USA
2. Department of Mathematical and Computational Sciences, NIT Karnataka, Mangalore, 575 025, India - 刊物主题：Mathematics, general;
- 出版者：Springer Berlin Heidelberg
- ISSN：2193-5351
文摘
We present a local convergence analysis for eighth-order variants of Newton’s method in order to approximate a solution of a nonlinear equation. We use hypotheses up to the first derivative in contrast to earlier studies such as Amat et?al. (Appl Math Comput 206(1):164-74, 2008), Amat et?al. (Aequationes Math 69:212-13, 2005), Chun et?al. (Appl Math Comput. 227:567-92, 2014), Petkovic et?al. (Multipoint methods for solving nonlinear equations. Elsevier, Amsterdam, 2013), Potra and Ptak (Nondiscrete induction and iterative processes. Pitman Publ, Boston, 1984), Rall (Computational solution of nonlinear operator equations. Robert E. Krieger, New York, 1979), Ren et?al. (Numer Algorithms 52(4):585-03, 2009), Rheinboldt (An adaptive continuation process for solving systems of nonlinear equations. Banach Center, Warsaw, 1975), Traub (Iterative methods for the solution of equations. Prentice Hall, Englewood Cliffs, 1964), Weerakoon and Fernando (Appl Math Lett 13:87-3, 2000), Wang and Kou (J Differ Equ Appl 19(9):1483-500, 2013) using hypotheses up to the seventh derivative. This way the applicability of these methods is extended under weaker hypotheses. Moreover, the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study.