Paper:
Finding All Solutions of Systems of Nonlinear Equations Using Spiral Dynamics Inspired Optimization with Clustering
Kuntjoro Adji Sidarto and Adhe Kania
Department of Mathematics, Institut Teknologi Bandung
Bandung 40132, Indonesia
- [1] K. Tamura and K. Yasuda,“Spiral Dynamics Inspired Optimization,” J. of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Vol.15, No.8, pp. 1116-1122, 2011.
- [2] Y. Z. Luo, G. J. Tang, and L. N. Zhou, “Hybrid approach for solving systems of nonlinear equations using chaos optimization and quasi-Newton method,” Applied Soft Computing, Vol.8, pp. 1068-1073, 2008.
- [3] R. L. Burden and J. D. Faires, “Numerical Analysis,” 7th ed., Brooks/Cole, 2001.
- [4] I. G. Tsoulos and A. Stavrakoudis, “On locating all roots of systems of nonlinear equations inside bounded domain using global optimization methods,” Nonlinear Analysis: Real World Applications, Vol.11, pp. 2465-2471, 2010.
- [5] W. F. Sacco and N. Henderson, “Finding all solutions of nonlinear systems using a hybrid meta-heuristic method with Fuzzy Clustering Means,” Applied Soft Computing, Vol.11, pp. 5424-5432, 2011.
- [6] C. Grosan and A. Abraham, “A new approach for solving Nonlinear equations systems,” IEEE Trans. Systems, Man and Cybernetics, Vol.38, No.3, pp. 698-714, 2008.
- [7] W. Song, Y. Wang, H. X. Li, and Z. Cai, “Locating multiple optimal solutions of nonlinear equations systems based on multi objective optimization,” IEEE Trans. Evol. Comput., in press.
- [8] V. Aggarwal, “Solving transcendental equations using Genetic Algorithm,” http://web.mit.edu/varuntextunderscore ag/www/stetextunderscore gas.pdf
- [9] R. Seydel, “Tools for Computational Finance,” Springer-Verlag, 2002.
- [10] S. Joe and S. Y. Kuo, “Constructing Sobol sequences with better two dimensional projections,” SIAM J. Sci. Comput., Vol.30, pp. 2635-2654, 2008.
- [11] K. Chen, P. Giblin, and A. Irving, “Mathematical Explorations with MATLAB,” Cambridge University Press, 1999.
- [12] S. Krzyworzcka, “Extension of the Lanczos and CGS methods to systems of nonlinear equations,” J. Comput. Appl. Math., Vol.69, No.1, pp. 181-190, 1996.
- [13] R. B. Kearfott, “Some tests of generalized bisection,” ACM Trans. Math. Softw., Vol.13, No.3, pp. 197-220, 1987.
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.