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A Two-Point Newton Method Suitable for Nonconvergent Cases and with Super-Quadratic Convergence
Joint Authors
Ndlela, W. N.
Nkambule, S. J.
Tiruneh, Ababu Teklemariam
Source
Advances in Numerical Analysis
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-03-19
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
An iterative formula based on Newton’s method alone is presented for the iterative solutions of equations that ensures convergence in cases where the traditional Newton Method may fail to converge to the desired root.
In addition, the method has super-quadratic convergence of order 2.414 (i.e., 1+2).
Newton method is said to fail in certain cases leading to oscillation, divergence to increasingly large number, or offshooting away to another root further from the desired domain or offshooting to an invalid domain where the function may not be defined.
In addition when the derivative at the iteration point is zero, Newton method stalls.
In most of these cases, hybrids of several methods such as Newton, bisection, and secant methods are suggested as substitute methods and Newton method is essentially blended with other methods or altogether abandoned.
This paper argues that a solution is still possible in most of these cases by the application of Newton method alone without resorting to other methods and with the same computational effort (two functional evaluations per iteration) like the traditional Newton method.
In addition, the proposed modified formula based on Newton method has better convergence characteristics than the traditional Newton method.
American Psychological Association (APA)
Tiruneh, Ababu Teklemariam& Ndlela, W. N.& Nkambule, S. J.. 2013. A Two-Point Newton Method Suitable for Nonconvergent Cases and with Super-Quadratic Convergence. Advances in Numerical Analysis،Vol. 2013, no. 2013, pp.1-7.
https://search.emarefa.net/detail/BIM-490640
Modern Language Association (MLA)
Tiruneh, Ababu Teklemariam…[et al.]. A Two-Point Newton Method Suitable for Nonconvergent Cases and with Super-Quadratic Convergence. Advances in Numerical Analysis No. 2013 (2013), pp.1-7.
https://search.emarefa.net/detail/BIM-490640
American Medical Association (AMA)
Tiruneh, Ababu Teklemariam& Ndlela, W. N.& Nkambule, S. J.. A Two-Point Newton Method Suitable for Nonconvergent Cases and with Super-Quadratic Convergence. Advances in Numerical Analysis. 2013. Vol. 2013, no. 2013, pp.1-7.
https://search.emarefa.net/detail/BIM-490640
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-490640