Home   >   CSC-OpenAccess Library   >    Manuscript Information
An Improvement to the Brent’s Method
Zhengqiu Zhang
Pages - 21 - 26     |    Revised - 01-05-2011     |    Published - 31-05-2011
Volume - 2   Issue - 1    |    Publication Date - May 2011  Table of Contents
Brent’s Method, Simplification, Improvement
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.
CITED BY (8)  
1 Wagner, C. F. (2015). Improving shock-capturing robustness for higher-order finite element solvers (Doctoral dissertation, Massachusetts Institute of Technology).
2 Gómez, Y. Z. O., Montilla, C. A. L., & Rodas, C. F. R. (2014). Herramienta de Entrenamiento Virtual en 2-D para Rehabilitación de Motricidad Fina en Miembro Superior con Incorporación de un Dispositivo Háptico (2-D Virtual Training Tool for Fine Motor Rehabilitation in Upper Limb using a haptic device/Virtual Ferram). Revista Ingeniería Biomédica,
3 Ordoñez, Y. Z., Luna, C. A., & Rengifo?, C. F. Herramienta de Entrenamiento Virtual en 2-D para Rehabilitación de Motricidad Fina en Miembro Superior con Incorporación de un Dispositivo Háptico (software para rehabilitación fina en miembro superior).
4 Krishnamurthy, L. Root Finder Framework.
5 Stage, S. A. (2013). Comments on an improvement to the Brent’s method. International Journal of Experimental Algorithms, 4(1), 1-16.
6 Gomes, A., & Morgado, J. (2013). A generalized regula falsi method for finding zeros and extrema of real functions. Mathematical Problems in Engineering, 2013.
7 Braun, V., Flegel, S., Gelhaus, J., Möckel, M., Kebschull, C., Radtke, J., ... & Vörsmann, P. (2013). Orbital lifetime estimation using ESA’s OSCAR tool.
8 Ou, G., Chen, X., Kilic, A., Bartelt-Hunt, S., Li, Y., & Samal, A. (2013). Development of a cross-section based streamflow routing package for MODFLOW. Environmental Modelling & Software, 50, 132-143.
1 Google Scholar 
2 CiteSeerX 
3 refSeek 
4 Scribd 
5 SlideShare 
6 PdfSR 
Alfio Quarteroni, Fausto Saleri. Scientific Computing with MATLAB (Texts in Computational Science and Engineering 2), Springer, 2003, pp.52.
Antia,H.M., Numerical Methods for Scientists and Engineers, Birkhäuser, 2002, pp.362-365,2 ed.
Brent, R.P., Algorithms for Minimization without Derivatives, Chapter 4. Prentice- Hall, Englewood Cliffs, NJ. ISBN 0-13-022335-2,1973.
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.
Jaan Kiusalaas. Numerical Methods in Engineering with Python, 2nd Edition, Cambridge University Press, 2010.
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.
Ridders, C.J.F. “ Three-point iterations derived from exponential curve fitting ”, IEEE Transactions on Circuits and Systems 26 (8): 669-670,1979.
Wikipedia contributors. “ Brent's method. Wikipedia ”, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 13 Apr. 2010. Web. 13 May. 2010.
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.
Dr. Zhengqiu Zhang
- China

View all special issues >>