A New Verified Method for Solving Nonlinear Equations
Commenced in January 2007
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Edition: International
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A New Verified Method for Solving Nonlinear Equations

Authors: Taher Lotfi , Parisa Bakhtiari , Katayoun Mahdiani , Mehdi Salimi

Abstract:

In this paper, verified extension of the Ostrowski method which calculates the enclosure solutions of a given nonlinear equation is introduced. Also, error analysis and convergence will be discussed. Some implemented examples with INTLAB are also included to illustrate the validity and applicability of the scheme.

Keywords: Iinterval analysis, nonlinear equations, Ostrowski method.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1056036

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References:


[1] G. Alefeld, J. Herzberger, Introduction to Interval Computations, Academic Press, New York, 1983.
[2] M. Grau, J. L. Diaz-Barrero, An improvement to Ostrowski root-finding method, Appl. Math. Comput. 173 (2006) 450-456.
[3] J. Kou, X. Wang, Some improvements of Ostrowski-s method, Appl. Math. Lett. 23 (2010) 92-96.
[4] R.E. Moore, Interval Analysis, Prentice-Hall, Englewood Cliff, NJ, 1966.
[5] R. E. Moore, R. B. Kearfott, M. J. Cloud, Introduction to Interval Analysis, SIAM, 2009.
[6] A. Neumaier, Interval Methods for Systems of Equations, Cambridge University Press, 1990.
[7] A.M. Ostrowski, Solution of Equations in Euclidean and Banach Spaces, third ed., Academic Press, New York, 1973.
[8] S. Rump, INTLAB - INTerval LABoratory, in Developments in Reliable Computing, T. Csendes, ed., Kluwer Academic Publishers, Dordrecht, 1999, pp. 77-104. http://www.ti3.tu-harburg.de/rump/. 2