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| An Improvement to the Brent’s Method
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Full
text: |
 PDF(74.6KB) |
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Source |
International Journal of Experimental Algorithms (IJEA) |
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Table of Contents |
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Volume: 2 Issue: 1 |
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Pages: NULL |
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Publication
Date: March / April 2011 |
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ISSN
(Online): 2180-1282 |
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Pages |
21 - 26 |
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Author(s) |
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Published
Date |
31-05-2011 |
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Publisher |
CSC
Journals, Kuala Lumpur,
Malaysia |
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ADDITIONAL
INFORMATION |
| Keywords Abstract References Cited by Related Articles Collaborative
Colleague |
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KEYWORDS: Brent’s Method, Simplification, Improvement |
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| This study presents an improvement to the Brent¡¯s Method by reconstruction. The Brent¡¯s Method determines the next iteration interval from two subsections, whereas the new method determines the next iteration interval from three subsections constructed by four given points and thus can greatly reduce the iteration interval length.
The new method not only gets more readable but also converges faster. An experiment is made to investigate its performance. Results show that, after simplification, the computational efficiency can greatly be improved.
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| 1 |
Brent, R.P., Algorithms for Minimization without Derivatives, Chapter 4. Prentice- Hall, Englewood Cliffs, NJ. ISBN 0-13-022335-2,1973.
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| 2 |
Antia,H.M., Numerical Methods for Scientists and Engineers, Birkhäuser, 2002, pp.362-365,2 ed.
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| 3 |
Dekker, T. J. Finding a zero by means of successive linear interpolation, In B. Dejon and P. Henrici (eds), Constructive Aspects of the Fundamental Theorem of Algebra, Wiley- Interscience, London, SBN 471-28300-9,1969.
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| 4 |
Alfio Quarteroni, Fausto Saleri. Scientific Computing with MATLAB (Texts in Computational Science and Engineering 2), Springer, 2003, pp.52.
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William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery. Numerical Recipes in C, The Art of Scientific Computing Second Edition, Cambridge University Press, November 27, 1992, pp. 358–362.
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| 6 |
Ridders, C.J.F. “ Three-point iterations derived from exponential curve fitting ”, IEEE Transactions on Circuits and Systems 26 (8): 669-670,1979.
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Jaan Kiusalaas. Numerical Methods in Engineering with Python, 2nd Edition, Cambridge University Press, 2010.
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| 8 |
Wikipedia contributors. “ Brent's method. Wikipedia ”, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 13 Apr. 2010. Web. 13 May. 2010.
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| 9 |
Press, W.H.; S.A. Teukolsky, W.T. Vetterling, B.P. Flannery. Numerical Recipes in C: The Art of Scientific Computing (2nd ed.). Cambridge UK: Cambridge University Press.1992, pp. 358–359.
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| Zhengqiu Zhang : Colleagues
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