A New Verified Method for Solving Nonlinear Equations
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.
[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
[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
@article{"International Journal of Engineering, Mathematical and Physical Sciences:51021", author = "Taher Lotfi and Parisa Bakhtiari and Katayoun Mahdiani and Mehdi Salimi", title = "A New Verified Method for Solving Nonlinear Equations", 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.", volume = "6", number = "4", pages = "394-3", }